Missing Photoshop Color Space Profile

I have a feeling this is about files coming from Lightroom as ProPhoto (which they do by default) - and the OP mistakenly thinking that Photoshop's working space needs to match. Which it doesn't.

This is an extremely common misunderstanding.

That said, I have seen a couple of instances where the ProPhoto profile is actually missing from the list. Profiles are installed in a system folder, so first check if it is here:

However, profiles are also copied to a separate Adobe folder, which is here:

This is where the list originates. You can see the "recommended" subfolder has its own section in the list. So if ProPhoto is missing from the list, try to copy it from the system folder into the "recommended" folder.

Edit>Convert to Profile

However ProPhoto RGB is missing from the drop-down list of options in my Photoshop.

Could you clarify what dialog you are in? To set the application's default RGB profile (the RGB Profile that is used when you create a new document), you have to select the Edit>Color Settings>Working Spaces>RGB drop down

You don't need to do that. The embedded profile will always take precedence and override the working space. There's no need for them to match.

With that out of the way, scroll down the list and you'll probably find PP further  down.