The P0605 indicates that the Transmission Control Module (TCM) is faulty.Replace the Transmission Control Module. The fault is for a internal Transmission Control Module failure. There is nothing external that can cause this code.
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P0605 is for internal PCM failure, not TCM.
You need to replace the PCM. You say you already did, but it must be a new one from Chrysler, or you will get this code from a used or rebuilt unit..