How do I get old photos back on my iPhone?

If you were using iCloud Photos on the old phone, your photos should be in iCloud – from where your new iPhone, your computer, and/or the iCloud Web interface can pick them up. Once you connected a new iPhone to the same Apple ID / iCloud account, turned on iCloud Photos, and gave it a chance to start syncing with iCloud, your photos would start to appear on the new iPhone. And you could check the iCloud Web interface even before then.

https://www.icloud.com/

If you were not using iCloud Photos on the old phone, then

• If you had backed up the lost phone, and had not excluded photos from backups, you might be able to get those photos back by restoring your backup to another phone. (You can set backups to happen automatically when an iPhone is connected to Wi-Fi Internet service and power, so you might have a backup even if it's been some time since you manually triggered one.)

If your photos were not in iCloud Photos or in an iPhone backup, then, unless you've copied/imported them to some other place, they're gone.

Any photos available to you are at iCloud.com/photos or on your device(s).

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What does that have to do with photos?