回复：老板突然翻脸，敬请帮助指教！急急急！！！

If the Human Resources of A University do not report your leaving to USCIS before B University file the H-1B transfer petition for you, everything will be OK. From my point of view, mostly likely the Human Resources of A University will not do that within one to two month, especially in the summer time.

So just go ahead to do the H-1 transfer and nothing worried about.