I'll assume that you have correctly identified your father's retirement account as being a traditional IRA and not an account like a 401(k) in an employer plan.
With no Form 1099-R for the movement of the funds to your mother's IRA, this was apparently appropriately done as nonreportable a trustee-to-trustee transfer (not a direct rollover; a trustee-to-trustee transfer of an IRA is neither a distribution nor a rollover).
Code G is never to be used to report the movement of funds from one IRA to another.
Just report the code-4 Form 1099-R.
