Handstand to freestanding HSPU

What additional elements are needed to get from a freestanding handstand to a freestanding HSPU? Is it just triceps strength? So for example, what would happen if I would develop a solid handstand and would get to 20 easy Ring Dips with proper technique (rings turned out at support position)? Would I be able to do a freestanding HSPU without specifically practicing for it?

 

Thanks in advance

no, free hspu must be trained specifically.

the pressing itself is not hard and should be asy for someone doing 20 good ring dips. building the awareness to keep a good line while lowering is infinite times harder than the pressing itself.