I just checked my spare hose and it appears to be a standard short Schrader valve core used auto tires. I compared it to a valve I had here and it appears that the Partner one may have a slightly longer center pin. I would call them and check but should be an easy fix. Just unscrew the old one and install the new core, mine was tight but came out with a little force.
It is a good idea to replace the o rings on the stove end of the hose every so often, they have the proper size in the repair kit or you can buy them at the hardware store if you can match the size.
I did buy a couple of new hoses from Partner a few years ago, they weren't very expensive, I just bought the two that connect to the stove not the entire regulator and hose assembly.