Who may put the eucharist in the tabernacle?

is it proper for altar servers to put holy eucharist in tabernacle after communion?

GIRM # 163:

When the distribution of Communion is finished, the priest himself immediately and completely consumes at the altar any consecrated wine that happens to remain; as for any consecrated hosts that are left, he either consumes them at the altar or carries them to the place designated for the reservation of the Eucharist.

It is not proper for altar servers to place the Eucharist in the tabernacle following communion at Mass.

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