Can I Back Up an iPhone With a Broken Screen Before Moving to a New Phone?

Check your Apple account from a computer and see whether you can free up iCloud space or temporarily upgrade the storage. The extra space can allow the old phone to finish backing up, and newer iPhones may provide temporary storage for migration. However, neither option can recover data that was never synced or backed up, and the transfer may still require interacting with the old phone's screen and approving the connection.

Your best chance is to leave the damaged iPhone connected to its charger and Wi-Fi and increase your iCloud storage so it has room to complete a backup. The new iPhone may also offer temporary iCloud storage for transferring data. Set up the new phone without erasing or replacing anything yet, then check whether a newer backup appears. This will only work if the old phone is still unlocked, connected to Wi-Fi, and able to start an automatic backup.

Be careful about restarting the damaged phone. After a restart, iOS normally requires the passcode before Wi-Fi and automatic backups can function again, and you may not be able to enter it with the broken display. Keep it powered and avoid making changes unless you know you can unlock it.