@LaPaTa: From your description it sounds like you’re not copying the secret/private key from your computer to your Android device, only the public key. Please make sure to follow these instructions: What is the best way to transfer my own key to OpenKeychain?
Edit: If you’re using Thunderbird’s built-in OpenPGP support, open the “OpenPGP Key Manager”, select your own key, then select “Backup Secret Key(s) To File” from the “File” menu.