This question is essentially communal, and its ramifications for the community’s identity, cohesion, and avodat Hashem play a major part in any decision. Arriving at a balanced decision entails consultation with a local religious authority who is in position to judge what will be of most spiritual benefit to the specific community. In cases like these, communal customs and norms can have greater halachic weight than written sources.Our response is intended as a preliminary discussion of the general issues.
There are a few different pieces to this question. On a strict halachic level, once tefilla is clearly over, members of each gender can enter the other’s space. In a synagogue in which speaking by the Aron Kodesh is strongly associated with the rabbi, a slightly different location may be preferred for any lay speaker.
A woman, speaking to a congregation in the synagogue right after tefilla does raise sensitivities, though. Rav Moshe Feinstein (OC 5:12:3) maintained that a woman could teach Torah to a mixed group after tefillot on an occasional basis. He added, however, that the teaching should be in a private home rather than in a synagogue space, and only with the speaker sitting down. Unfortunately, he does not explain these caveats or their halachic force beyond mentioning “greater modesty.”
Rav Aharon Lichtenstein was reportedly not in favor of women speaking directly after synagogue in his neighborhood, though reportedly he did not view such teaching as prohibited, but more as a matter that went against communal and religious sensitivities.
Many communities, Rav Lichtenstein’s included, do have women sometimes teach a communal shiur in synagogue following prayer. Where that reflects the contemporary communal values of the particular congregation, it is not halachically objectionable, and can be positive and important. Some communities that have women speak in this context pause slightly after tefilla ends and announcements have been made to make it clear that the formal prayer service has ended and the communal shiur is beginning (and sometimes also to make adjustments to the mechitza or to seating to enable women to hear the shiur more optimally). Some have a woman speak from a different location in the synagogue. These choices, too, depend on the specific community involved.