Not sure what your question is. What its seems like is that John Doe created a trust for the benefit of Jim Doe and named Jack Doe as trustee of that trust. That is perfectly fine if that is in fact the case.
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I agree that your question is not entirely clear. U/A is a common abbreviation used when referring to a trust agreement. If Jack Doe is acting as Trustee of the John Doe Living Trust, then the above caption would appear to be fine.
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Yes, U/A is a short hand (and common) way of saying the John Dow Living Trust under the trust agreement executed on 12/12/2002.
Many times financial institutions will use this method to name counts owned by trusts