The rail options are: 20:31 Sky Access train to Takasago and change to a Haneda-bound train, or 20:44 Narita Express to Shinagawa and change to a Haneda Keikyu train. Both options will arrive at Haneda at 22:22.
The change at Takasago is on the same platform, by far the easiest route other than the direct train or bus.