It should be the person overseeing the work, If the Soldier is not coming back to your section the records should be transferred to the new leader.
If he is coming back to your section you might want to consider doing the counseling yourself, if the other leader is not doing it.
It would also be wise to ask the senior leader in charge of you how he/she would like the issue handled. Then prepare an MFR include the date/time/information in your MFR., stating that the Soldier was reassigned to another section.
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