Crediting a postdoc on a grant
JJ is a postdoctoral reearcher, who works for Professor Obb. Professor Obb is high-up in the department meaning that he does little research himself any more and leaves his postdocs to largely to carry out their own independent research in the lab. During the course of his research, JJ comes up with a new direction, which gives rise to a couple of research papers that are coauthored with Professor Obb. JJ also writes a grant application to provide new funding for his own position in the future on which Professor Obb is a co-PI. This doesn't get funded and eventually through lack of funds JJ leaves the lab. Some time later he discovers that Professor Obb has resubmitted his ideas alone, only making changes where referees had indicated they were unhappy on the original grant application. This time Professor Obb receives funding and employs another postdoc on the money, even though he knows JJ has no job at this time.
Does JJ's presence in Professor Obb's lab and his earlier coauthorship / proposed sharing of PI-status mean that Professor Obb is entited to reapply for funding?
If JJ continues to work in this research area, can he continue to use the ideas in the grant even though he knows somebody else is working on them.
The new postdoc asks for advice, because she is not very familiar with the subject area. What should JJ do?