Can you help determine how to remove old shower valve, cross handle, no screws?

[BrooklynOrange]

Hello. I have an old shower valve that needs replacing. No product name, or set screw. It's got a cross handle with a diverter above the handle. My plumber thought it was similar to an American Standard T0646002.002 (except cross handle not a bar) but the insides are not the same. This was in place when I bought the unit, and it's hard to say how long it's been here. Building goes back to 1964.

He can't find any screws or anything indicating how to remove it. Component pieces simply turn loosely. No caps or anything else that open. Not sure this image link will work:
file:///Users/lgibbs/Downloads/ShowerFaucet1.jpg

Thank you, Lisa

 

[Deleted member 120897]

Not sure this image link will work:
file:///Users/lgibbs/Downloads/ShowerFaucet1.jpg

Thank you, Lisa

I couldn’t open it.