Those are likely type 1 (very early) plastic grips. They are rare and are very valuable. Think a few hundred dollars. They were used by Krieghoff and (in a very limited way) tested at Mauser.
The Mauser "hump" started in mid 1937.
Take a look inside the side plate and see if the number "62" or "63" is in there. If so, it's a matching Mauser plate. IIRC a few that year might not have numbers inside.
All the numbering dies that I can see (except for the toggle train) look like Mauser die stamps. The receiver proof and acceptance is, of course, Mauser as well - except the E/2 on the toggle.
The "R" on the tang of the middle toggle is interesting. I wonder if this somehow marked an armorer's replacement or some kind of "Revision control" work at an armory or higher level repair facility? It certainly looks to be in excellent condition, and some kind of facility work within the Luftwaffe could account for the toggle train and grips.
I personally would not change a thing about it. It is how your Grandfather kept it.
If you want an all matching gun, just purchase one instead of chasing the parts.
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 Igitur si vis pacem, para bellum -
- Therefore if you want peace, prepare for war.
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