One partner bought out another partner's interest in old LLC and move to a new LLC, do I need to report this in the old LLC final return?

The way I am interpreting this is there is a 2 member LLC being taxed as a partnership.  One partner buys out the other partner and they dissolve that old 2 member LLC.  There will be a final partnership return filed for old LLC.  They actually both likely had their % ownership on the date it was finalized so you do not need to put 0% on each K-1.  The final box will be checked on the 1065 and respective k-1s.

Then the remaining "partner" forms a single member LLC because it is no longer a partnership.  That new LLC may elect to be taxed as a corporation then an S-corp if it files form 2553 and 8832.  Otherwise a single member LLC will default to being taxed as a sole proprietorship, Sch C.