No, putting an already frozen item into a freezer will not make it freeze faster. In fact, it will not significantly affect the freezing time at all. Freezing is a process that involves transferring heat from the object to its surroundings until it reaches the freezing point and solidifies.
When you place a frozen item in a freezer, the freezer's cold air will work to maintain its low temperature. However, the already frozen item will not contribute much heat to the freezer since it is already at a very low temperature. The freezer will need to remove the remaining heat from the surroundings and the item itself to continue freezing it further.
The freezing process will continue at its usual rate, determined by factors such as the initial temperature of the item, its size, and the efficiency of the freezer. Placing an already frozen item in the freezer will not speed up this process since the freezer needs to maintain a consistent temperature to freeze items properly.