It's kind of a long process, and it really depends on the phone you have. Here's what I did to do a transfer dump of photos to my newer phones. Keep in mind I did this with an Android, my steps may not be helpful if you have an Apple phone.
1. Request a Data Report from Facebook. This may take 24-48 hours to do so.
2. Once you get that report, it'll have files dedicated to photos uploaded either via browser, messenger, etc.
3. Pick the photos you want.
4. Transfer them on to a cloud service that is accessible both by your computer and phone.
5. Access Cloud Service on your phone.
6. Download those photos to your phone.
And voila! The photos you wanted will be there. There is one cavat though: Facebook labels your photos with data labels instead of titles, so you might want to take the time to label your files correctly before transferring them to a cloud service. There's also the option of doing a transfer by plugging in your micro SD card into the computer, but mine doesn't have a slot and I didn't have a SD-to-mirco SD adapter at the time.