I didn't do a super-careful read-through and maybe there are better people here to help you with the specifics, but I'm impressed. The points I have to make are all pretty simple, you can take them or leave them.
In the first paragraph you say "may fulfill." My advice (it's only advice) is to avoid sounding uncertain. Drop the 'may' and say that it fulfills the requirements, period.
In the second paragraph, you say "experience on. . ." I'd suggest you say "experience with. . ." Also, I'm not sure that "On my . . . degree" sounds good. Maybe it's American to say something like "In my degree" or "while studying for. . . . I specialized in. . ."
In the third paragraph, I suggest finding alternatives for "got the maturity to decide" (was mature enough to decide? had enough experience to decide?) and "Which area I pretend to be specialized." (Maybe: I had enough experience to decide on the area I would pretend to be specialized in. But, in a letter of this tone, I'd suggest dropping the humorous reference to pretending, even if it's meant to be modest.) Also, my skills IN project management (not on).
Like I said: this is just my feeling. Writing these letters can be an art, but I'm not that kind of artist.
- For Teachers