Does the reply to the Message cantrip have a time/distance limit?

The message cantrip says the following:

You point your finger toward a creature within range and whisper a message. The target (and only the target) hears the message and can reply in a whisper that only you can hear.

The spell itself has a duration of 1 round and a range of 120 feet, but I assume this is for the caster’s “outgoing” message. Is there a time limit or a distance limit on the recipient’s reply?

I ask this because a player claims that the recipient of the message can reply any time in the future at any distance, because the spell does not specify that, and they have therefore used the message cantrip as a way to have an NPC tell them when someone is ready to collect (i.e. casting message on the NPC, with the message being “reply to this message spell when you’re done“).

I believe that the intent is that the recipient is expected to reply straight away, but that isn’t specified. For contrast, the sending spell does specify when the recipient is allowed to respond:

You send a short message of twenty-five words or less to a creature with which you are familiar. The creature hears the message in its mind, recognizes you as the sender if it knows you, and can answer in a like manner immediately.

Sending says that the recipient must reply immediately, whereas message does not specify when the recipient must reply, hence my player claiming that there is no time limit.

Regarding the distance thing, this is also treading on the toes of the sending spell somewhat, except that the caster of message still has to be within 120 feet of the recipient (it’s only the recipient that seems to have no limit on distance), whereas sending allows the caster to be the one to initiate long-distance communication.

Is my player correct? Can the recipient of a message really reply after any length of time after they receive the message, and over any distance?