After I install the iOS 13, I no longer can assign photos to different albums

This works for me in iOS 13.1:

Tap a photo or video to view it in full screen. Tap , tap Add to Album, then select the album you want to add it to.

It doesn't move the photo, but adds it to a another album. You can then delete the photo from the original album if you like.

Hey, mw128.

I see that you're unable to relocate a photo to a different album in the Photos application on your iPhone, and I'm glad to help.

Organize photos in albums on iPhone -- This article provides the information and steps that you need to add photos and videos to a different album.

If this doesn't correct the problem, please describe the issue in greater detail. Please include the text of any messages you receive. The more information you provide, the better we'll be able to offer additional guidance.

Take care.

Thanks for getting back to us, mw128. It's appreciated. Since you're unable to use the steps provided in the article, I'd like you to contact Apple Support.

Apple - Support - Product Selection — After selecting this link, choose Apps & Features > The topic is not listed. Type a brief description of the issue, then select how you'd like to start the conversation.

Cheers!