Welcome to the Apple Support Communities!
I understand you would like to save your Facebook photos to your iPhone. The first thing to check is to make sure your settings allow Facebook. Open the Settings app and choose Settings > Privacy > Photos. Select Facebook and choose Read and Write.
Here is some information from Facebook for saving photos:
https://www.facebook.com/help/iphone-app/155361567863444?helpref=uf_permalink
Take a look at this resource and let us know if you are able to get your photos on your iPhone.
Have a great day!