I would download the attached photo first (or save to device). Then go to your Gallery app, select the photo, tap Share, and then Upload to Photos.
If you have Google Photos Autobackup turned on, then the photo might have already uploaded to Google Photos, depending on if the folder you downloaded it to is set to auto backup. Open the Photos app, swipe in from the left, and tap Device Folders. Look for the folder where the downloaded photo is, and see if the cloud icon is blue. If it isn't, tapping the cloud will turn on autobackup for that folder.
I understand that the photo is an attachment--but you still have a Share option. What options are listed when you tap Share? What can you share to?
If you save the photo to the device, can you find it in a directory when you use My Files?
After I click on SHARE, the next screen offers many choices to Share to, but GOOGLE PHOTOS is not one of them. Any other suggestions?
BTW, I use the SAVE TO DOWNLOAD, the file gets downloaded and I can move it into Google photos. It's the SHARE command I'm trying to get to work correctly.
Verizon Samsung Galaxy S5 Lollipop 5.0
Ok, one other thing I asked before--do you have the Google Photos app installed?