Hello all, I agree with both Shaun and DC.
Actually we have seen not just the 510.50x mixing Heuer and TAG-Heuer parts (typically crown and clasp), but also same-period L5100 Carreras (510.511 and 510.523).
The most usual mix is:
- TH clasp on Heuer watch
- Heuer crown on TH watch

So indeed yours may well be an original part, and some even call this period the 'transitional period' as if it were art history!
But IMHO in spite of its being genuine a TH-signed part mounted on a Heuer watch has a somewhat lower value than a wholly Heuer counterpart.
Cheers.
Fabrizio