Turkish citizen, US green card holder, but living in UK - Germany transit visa?

As long as he's not going on a Domestic flight he won't need a transit visa according Schengen Visa requirements from Germany:

Nationals from the above list are entitled to transit through the international transit zones without an airport transit visa:

1. If they hold a valid visa for the United States of America
2. If they return from the USA after having used the visa (however, the return has to occur within latest four days after expiration of the validity of the visa)

3. If they hold one of the following residence permits:

   • Form I-551 permanent resident card (valid for 2 to 10 years),
   • Form I-551 Alien registration receipt card (valid for 2 to 10 years),
   • Form I-551 Alien registration receipt card (no expiry date),
   • Form I-327 Re-entry document (valid for two years — issued to holders of a I-551),
   • Resident alien card (valid for 2 or 10 years or no expiry date. This document guarantees the holder’s return only if his stay outside the USA has not exceeded one year),
   • Permit to re-enter (valid for two years. This document guarantees the holder’s return only if his stay outside the USA has not exceeded two years),
   • Valid temporary residence stamp in a valid passport (valid for one year from the date of issue).