There are myriad ways to express a sentiment similar to the one you describe. Here are a few examples:
The above is purely for your information.
This is solely by way of information.
I write this simply to keep you informed of the situation.
. . . keep you apprised . . .
. . . keep you in the loop.
In my experience (mainly in the world of business), including this sort of phrase in a letter serves to clarify that the recipient is not expected to take specific action at this time. If you want a more general phrase to accompany an informative letter, you might also try:
I hope you find this useful.
By way of agreement with commenter jmoreno, I will add that the most similar practice I have observed in AmE (especially in the business world) is to introduce information that is included purely for information's sake. Often this will occur as early as the subject line of an email, which could begin with “FYI:” without appearing too informal.
In the Cambridge Encyclopedia of the English Language (2003), thanks is considered a minor sentence, or more specifically, a type of minor sentence that is a "formula for stereotyped social situations."
In chapter 8 of "An Advanced English Grammar with Exercises" (1913):
Good usage does not demand that all sentences shall be absolutely complete. It often allows (and sometimes requires) the omission of words that, though necessary to the construction, are so easily supplied by the mind that it would be mere waste of time to utter them.
The first example of such an elliptical sentence is:
[I] thank you.
"Thank you" without an explicit subject has been used since at least the 15th century, according to an article in the ICAME Journal (vol. 26:63–80):
Interestingly, the shift from a clearly performative speech act with a subject, e.g. I thank you or I give thanks to you to the shortened forms thank you and thanks, had not gone far in Early Modern English. The shortened forms appeared in the 15th century and there are only five examples in my material [Corpus of English Dialogues].
So, although it is generally regarded as grammatically correct, it might sound too informal for business communications. That is entirely subjective, though. Of the alternatives you provided, I think the one beginning with "we" sounds best (see edit below):
We thank you for the information...
Alternatives to thank you can also give the letter a more professional tone:
We appreciate the information...
We are [very] appreciative of the information...
Our company is [very] grateful for the information...
Edit:
Rather than rely on my own assumptions, I tried to find more references for business writing etiquette with regard to thank-you letters or letters of appreciation. I think now that my opinion was wrong about the implied subject for thank you being too informal for business communications.
I found a reference from the American Management Association, The AMA Handbook of Business Writing (2010), which gives examples of several types of business letters. In it, there is an 8:3 ratio in favor of using the implied subject form, "Thank you," rather than for example, "I want to personally thank you..."
In another book with business letter examples, 300+ Successful Business Letters for All Occasions, the first example of a Thank-you letter (pg 51), begins with "Thank you..." The second example on page 52 also starts with the implied subject form, although the last sentence uses an explicit subject "We thank you..." The examples of other types of letters often use of the implied subject form, too.
Best Answer
I wouldn't say it's a tautology exactly, because you can write things other than letters. For example, you could write a book, a thesis, a play, or a poem, etc. In your example the fact you are writing a letter is obvious, since the reader will be reading the letter - therefore it's redundant.
If you do want to mention the letter, I wouldn't say "the letter", but "this letter". However, it's still redundant. I think it's better to leave it out. Take your friend's advice.