Rosa's theorem about tree T with m edges to decompose a complete with 2m+1 vertice

Question

In this theorem Rosa tell us that if there exist a tree T is graceful with m edges, then K_2m+1 could be decomposed into 2m+1 copies of tree T.

But I want to ask that should the 2m+1 copies be graceful?

Because I have seen some slide about it

the slide about decomposition

Some of copies satisfy this property but some of don't