Help to identify strap on Seamaster

Hello, I'm wondering if anyone can help me identify the strap on this Seamaster. The watch was a gift from my grandmother to my grandfather, probably in the sixties. I don't know if the strap is original so it could have been replaced over the years since then. I do love it but it's coming apart and I'm starting to consider how I might source a replacement. I haven't seen anything quite like it for sale yet but understandably the finish is likely to have altered through age and wear. Many thanks.

I was about to also solicit ideas for alternatives when you answered with such thoughts - much appreciated.

Yes it does (have the omega clasp) and yes definitely will transfer it. Many thanks for the thoughts