She is writing this letter because she wants the constitution to declare rights for women. The issue she identifies is women not being able to have a valid opinion just because she is a female, and also not being able express themselves as men at that time were able to.
Wollstonecraft sees this issue as a problem because she is a woman too and she knows the difficulties that women used to have at that time. She is part of the discourse community of women.
The Discourse community of Wollstonecraft are women in general because in the beginning of the letter she said that “I plead not for myself, but for my sex” meaning females.
I think that the recipient seems to be part of the discourse community, that is the reason why Wollstonecraft is explaining the problem to the recipient because if he were part of the discourse community he would not need someone to explain the issue to him