Research Supervision
I agree that the student should send off the manuscript, and notify both supervisors - whom I assume are members of the thesis committee - of having done so. The student might also communicate with supervisor A and the chair of the department in which the dissertation is being done, on the need for some guidance about how to proceed to meet the university requirement for publication. For instance, department guidance might stipulate that committee chairs are expected to assist students to submit manuscripts for consideration for publication by such-and-such a time in their graduate careers, in order to meet university requirements about this. It might assign a faculty advisor in the department to assist in this process, who can provide advice to students separate from their thesis committee members. There are a number of ways that department faculty can assume responsibilities to assist graduate students to meet their degree requirements, while not being on their committees.