Hey Dwight and Thor..!
Sorry for the delayed reply - but I saw this post yesterday AM - and figured I'd reply when I got back from a wedding we attended. Well - it was a rather long reception!!
Anyway - as you know, PX Lugers typically were numbered (large digets) - and were blued to a matching finish. As well, there are characteristics such as the toggle "machining" (many small parts were done by local SUHL machinists as the HK factory ran out of small parts in the construction of the PX Lugers), so there are some common aspects to these PX Lugers.
However - internally-numbered may have a "multi-finish" and are typicially a hodge-podge of specific parts - and are "post war parts" HKs. There is one aspect that bothers me from the photo - if you look at the sideframe - that alone is a different blue/finish from the rest of the frame - which instantly raises a red flag. It would be interesting to look at this one - and see what parts it contains.
The third are the GI built parts guns - and typically won't be "inscribed" - so again, it brings up that "red flag" noted above - but moreso, since both the side finish and inscription comes into question....
On the other hand, it would also be interesting to see what/if this one has for any provenance from the estate, and whether the estate has any documentation putting "HARGUS R. TYLER" in Suhl at 1945. If documemtation was available for that - it would still be interesting to closely examine this specific "example" - as well as the engraving techniue used on the name - and if any parts are internally numberd...???? My guess is that would be the only way to "verify" this piece...
Best to all..!!!
- John D.