The SPAB will tell you to dig up and resurrect the original carpenter
that built it.

Filler on its own will probably be of limited use, if the crack is
going to continue to move.

If you have the right skills and tools, look at pulling the crack
closed with clamps, then using large screws (countersunk under the
surface and capped with timber plugs), along with a waterproof glue
inside the crack.

Otherwise find a traditional joiner to make up a whole new piece, or
splice in a repair.

(actually to be fair to the SPAB, they will probably suggest the
latter. Their weekend courses in traditional building restoration are
very good, although they do tend to sneer at modern approaches widely
used by professionals)