Meisterwerke

a)

Last move could be Nc2xBa1+. Earlier in the game White captured bBc8 on c8, b6xNa7, c6xNb7, and gxPf, and promoted Pe2 on e8, while Black captured the h-pawn on its file and exPdxcxbxPa, and promoted Pg7 and Ph7 to bishops on g1 and h1. Solution: Retract Nc2xBa1, and play forward 1. Nca3+ Kb2,Kc1 2. Qc2#

b)

Last move could be gxf6 e.p.+, and it is possible to preserve White's castling right: White captured bBc8 on c8, b6xNa7, and gxPhxNg, and promoted on e8, while Black captured exPdxPcxbxa and g2xf1=B. (Or White captured the g-pawn on its file, axNb, b6xRa7-a8=R, and b6xNa7, and promoted on e8, while Black captured exPdxPcxbxa and hxg-g1=R). Solution: Retract g5xf6 e.p., and play forward 1. 0-0+ Bd1 2. Rxd1#.

Solution by Henrik Juel

The (b) solution doesn't work in (a), because there it is impossible to construct a game where wRh1 hasn't moved.
The (a) solution doesn't work in (b), because there promoting to B on e1 requires too many captures.