Puig's conjecture on source algebras of blocks

Let $F$ be an algebraically closed field of characteristic $p$, let $P$ be a finite $p$-group, and let $G$ range over finite groups containing $P$. An interior $P$-algebra is a source algebra of a block of $FG$ when it arises as the source algebra associated with that block.

Puig's conjecture. Given a finite $p$-group $P$, there are only finitely many isomorphism classes of interior $P$-algebras that are source algebras of a block of $FG$; here $G$ varies over all finite groups containing $P$.

This is a finiteness conjecture for source algebras of blocks in modular representation theory. The supplied text introduces it as one of the ingredients related to Feit's conjecture, but does not state its resolution in this generality.