It’s grammatically correct to use the word “self-explaining” in the sentence “Please find attached [a] self-explaining letter for your information and action.” After all, that word is synonymous with “self-explanatory.” “Self-explanatory” is more idiomatic, though, so I’d prefer using it in such sentences. In the second sentence you provided, I find the use of “self-explanatory” most appropriate: “Please find attached letter for your information, which is self-explanatory.” Simply for euphony’s sake, I would greatly hesitate to use “self-explaining” in such sentence constructions. Also, in my experience, people in professional circles simply won’t use “self-explaining” in such sentences; they’d use “self-explanatory” anytime.
