How can I synchronize my own movies

– The App Computer on the AppleTV box says: No mediathek and shows a spinning wheel

Check the settings on your Mac, as it has to be activated separately. See below.

– AirPlay is not possible: My iMac and the other devices are too far away

AirPlay is not direct communication. It still goes through your router, same as Home Sharing.

– Sharing with iCloud Photos is possible. Thank you for your hint. But I just want to sync my videos. The PhotoApp also loads my pictures into iCloud and that takes up a lot of storage space. And I am not sure, if the Photo App can handle long and HiRes Videos. I think, there are some limitations.

For videos in iCloud Photos, you will need a lot of iCloud storage.

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For Home Sharing, verify that the Mac is set to share content that is added to the TV app:

System Preferences﹥Sharing﹥☑︎ Media Sharing﹥Library name﹥…

System Preferences﹥Sharing﹥☑︎ Media Sharing﹥☑︎ Home Sharing

System Preferences﹥Sharing﹥☑︎ Media Sharing﹥☑︎ Home Sharing﹥(your matching Apple ID)

For Home Sharing, verify that the Apple TV is set to connect to the matching Apple ID account for Home Sharing:

Settings﹥Users and Accounts﹥[ᴀᴘᴘʟᴇ ᴛᴠ ᴀᴄᴄᴏᴜɴᴛs] Home Sharing﹥[your matching Apple ID]

The Apple IDs for Home Sharing have to match, or the client device won’t be able to load the library.

• Home Sharing. Note that viewing on an Apple TV box uses the Computers app for viewing, not the TV app. Note that Home Sharing is not available on third party devices. Use Home Sharing to share media from a computer to other devices - Apple Support
• AirPlay (to AirPlay-receiving devices, i.e. Apple TV box or AirPlay-enabled TV). Use AirPlay to stream video or mirror your device’s screen - Apple Support
• Share through iCloud Photos. Note that shared content will appear in the Photos app, not the TV app. Photos User Guide for Mac - Apple Support