I suggest doubt, and caution, about any such offers. At best, they might charge you a fee to "publish" on your behalf. They might just take the fee and disappear. If they do publish anything, it would likely be somewhere obscure that would not come to the attention of libraries, scholars in your field, or any other potential readers.

You could do an internet search for information about the sender of such mail, just in case it is a legitimate publishing house -- which I doubt. Sometimes, just typing the name into the search field, followed by the word "scam," will tell you all you need to know.

I agree with colleague Burke D. Grandjean, i.e. it is recommended to be a caution. Next, perhaps you may check is that publisher mentioned in the Beall's list (as potential predatory scholarly open-access publishers)?

https://beallslist.net/

There are indeed "ghost writers" who may write a book for you. This is a wide-spread service for politicians and celebrities to publish their autobiographies or other books. However, for science this is not a serious service, and the results may be of very low quality. There are even offers to write a graduation thesis for you, which is not only not serious, but illegal for you if you really submit this thesis. I agree with Burke D. Grandjean that you should be very cautious. There are other offers to do proofreading or improving the language of a book which you wrote yourself. These are usually serious.