Attached is the picture

Another picture; the white plastic item is what I want to replace on the other handle.

You may want to check this site: https://www.ereplacementparts.com/plumbing-parts.html

I have never used them for plumbing parts, but I have used them when I needed a part for my dishwasher and they were very helpful. You can call them and even send them an email with your picture above and I bet them would look into for you.

They have a good return policy; so, worse case scenario you could just older a part that looked similar and then send it back if it didn't work.