(What to do when someone wants to use your work in their book.)
As a general rule I'd say no. There are times when it is alright to say yes, but they are rare. From what you say, this guy does not appear to be going through any official channels to contact you, is that correct? By official channels I mean, he is the author of the book and asking to use your article in his book, correct?
The official way to send a request like this is an Acquisitions Editor of a Publishing House would write you a snail mail letter on official letter head. The letter would detail the book project, explain it's goals and marketing details. They would explain that the author had made a special request to include your article in the book.
There would be lots of "legal mumbu jumbo talk" written by publishing lawyers, to tell you your rights, what rights they would be buying (print, ebook, international, etc) and for how long (1 year, 7 years, life-time) they retained those rights before returning them to you (meaning you would have to take your article down off of your website, because you would no longer be the copyright holder even though you are the author, because by giving rights to the book publisher you effectively sold/rented your copyright holding to them).
Do keep in mind (and this is VERY important) that no one can publish your article ANYWHERE without you signing a copyright agreement contract, which grants them copyright permission. When someone asks to put your article in their book, what they are really asking is for you to give up your rights as an author, your copyrights, AND....
Very, very, very IMPORTANT: If you hand over something like "7 year print rights" they can print (and reprint) your article for 7 years without farther asking your permission AND if you put your article in print, they can sue you (and take everything you own) for copyright infringement, even though you are the original author, because when you gave them those "7 year rights" you handed the copyright ownership to them and you no longer have any right to use your own work.
This is very dangerous ground to walk on, because often times scam artists are well versed in these laws, yet authors are often clueless about these laws, and this is how scam artists swoop in and end up taking your life savings, your car, your house, and you could end up being the one in prison for copyright infringement, even though you are the author of the article.
This IS NOT a simple minor request this guy is asking for here. He is asking you to hand over your copyrights to him, and he is not using official channels (lawyers) to ask for your copyrights. nor is he offering you any advance or royalties (which is basically rental fees for use of your copyright.) NEVER give up your rights as an author!
The letter would also detail what kind of advance you would be receiving (about $500 is standard for using an article in a book; $2,000 to $7,000 is standard if you had written the entire book), along with what your royalty percentage is (usually .1% to 2% for minor contributors such as an article). They would also tell you the total amount of books they expect to sell in the next 3 years (most houses plan on 100,000 copies per year x .1% - 2% means you can expect to be paid about $100 to $2,000 a year for your contribution to the book.)
It is your right as the author of your article to be paid royalties whenever someone publishes your article ANYWHERE online or offline, but you can lose that right if you don't read all the fine print to the copyright law, contracts, and agreements before saying "yes" to someone's request to republish your work. Some publishing houses like Harlequin and Avon have eletronic contracts now, but by law you can request a paper contract mailed to you for signing and they will mail one out. It is your right as an author to request a hard copy to sign in person and no legitimate publisher is going to refuse to send one out.
Never trust a publisher that handles contracts and agreements via email and doesn't have the option to mail you a hard copy to sign in real ink. There has to be something in writing to make it legal, however, agreeing to an email is legally binding enough to cause you a $30,000 headache and a lot of months in the courthouse should you try to back out of the deal. Never sign anything or agree to anything until you have had a copyright lawyer and a publishing lawyer read the documents and go over what every line means with you.
Getting your article into another author's book can be a really good deal, more often than not though it will cause you far more harm than good. It's tricky business getting into these sorts of multi-authors in one book agreements. If not done with a lawyer over your shoulder every step of the way, you cold easily sign away and give up your rights as an author without even knowing that's what you had done!
Do know that it is INCREDIBLY RARE for a publishing house to contact you. So rare that most times you are contacted by a publishing house, you should assume it a scam and have your lawyer reply to the contact for you.
Included with the letter would be a bunch of legal documents, including a contract for you to sign (with your lawyer) and notarize, before sending it back to them.
As you did not mention receiving any of this, I am assuming you are dealing with a self-publisher? This is shaky ground. It could be okay or it could be a scam; most likely it's just someone who really has no clue what they are doing, and if they are not up on the legal issues enough to know how to contact you properly, they likely are also not up on the marketing issue enough to sell more than 100 copies of the book a year.
I often work with self-publishers and it can be a good thing if they actually know what they are doing and are running their self-publishing business professionally. Unfortunately, few fall into this category. There are only 2 times when I would recommend you work with a self-publisher on a deal like this:
1) You know them personally - they are a relative, friend from high school, co-worker, etc. Someone you know and trust and see face to face every day.
From what you say it sounds like this guy is a complete stranger to you. When it comes to publishing NEVER work with a stranger who's credibility you are uncertain of. EVER! A lot of authors get scammed this way. I've heard of authors losing $20,000, $200,000, and one who lost their home because of getting into deals like this that turned out to be really shady. In each case it started out simple, "Hey, I want to use your article in my book" but than the publisher would start asking for money "Hey I need $5,000 to run an ad for the book", etc. This is a VERY common scam.
2) You have heard of the author: you've read their books, you've seen them around on social networks, you know their product, you know they are running stable legitimate publishing business. (And they would have contacted you using official documents as described above.)
From what you say, this does not sound like what is happening.
So, yes, in your situation, I believe the best answer is NO, do not agree to his offer. It's too risky. You have too much to lose and there is nothing you will really gain.
Tell him, that after he publishes his book, to send you a free copy and you will read it and write a review for it on your site, in exchange for his putting a link /mention of your website in his book. This is a far better way for the two of your to "boost readership" to each other.
*source: I'm the editor-in-chief of a publishing house