I found a Solution in the apple forums:
https://discussions.apple.com/message/29256053#29256053
First pair the Aluminum Remote with the atv4, this can be done while Pressing (Menu + ->) for 6 seconds.
Then cover the IR receiver of the atv4 and press (Menu+Select) for 6 seconds to increase the id of the remote.
After this pair the remote with the atv3 via menu.
Make sure you have unpaid the remote at the atv3 bevor you increase the id or you can not control the atv3 anymore
😉 I have used the remote app in this case.