The security delay on the new organizer’s iPhone is expected. After an iPhone has been transferred or restored, Apple may need some time before recognizing it as a familiar device.
Once the delay has ended, go to the organizer’s iPhone and open:
Settings > Family > [child’s name] > Apple Account & Password > Change [child’s name] Password
Do not erase or reset the child’s iPhone while it is stuck on the iCloud sign-in screen. After changing the password, enter the new password on the child’s iPhone.
You can find Apple’s official instructions here:
Change your Apple Account password - Apple Support
A friendly note: This is the German-language Apple Support Community. Posting your question in German will make it easier for more members to understand it and offer assistance.