About 18 months ago I was flying HND-MUC-MAN with both legs on LH with an overnight layover in MUC. I wanted to check one bag through to MAN and another to MUC only because the smaller bag (carry-on size) contained liquid which I was taking for a friend in MUC. After a long discussion and a phone call to LH, I was told I could not split my bags. On arrival in MUC I claimed both bags and checked one of them immediately for the connecting flight the following day. I bought some liquid in a supermarket in MUC and checked the second bag before my flight back to the UK.

Assuming the same rule applies the OP will have to check all 3 bags to FRA, claim and check them again. No idea if NH operates the same rule.