Pelosi Bill Question

This isn't a proper diary.  And if I were REALLY sorry I wouldn't post it.  I just have a big question about procedure and I can't find the answer anywhere.  There must be a Kossack who knows!  If the Dems get rid of the filibuster, can the Dem Senate pass some of the many Pelosi bills from last session?  Or would the new House have to pass new bills first?