I don't believe the three piece set you show, with the exception of the G, was from the original Gerheart set.

The flour-de-lis and the "1" just don't match up with the "G". Besides the double ringed white "G" there is a brown rim single ringed "G". I would bet that there are two or three other rim colors of the "G". The Gerheart set would then be 4 or 5 colors of "G".

Now, over the course of 100 years chips get lost. I would say that chips were added to the surviving "G"s in order to make a poker set. So, the fleur-de-Lu's, "1" and "G" were found together in the Gerhard box but we're not all original to the set. Of course my opinion only.

I have probably a half dozen "sets" that were "made up" that are now considered original sets.

I've probably had this discussion with the "same collector" a dozen times

Unfortunately proving who is right is probably not possible.