There is an infographic for the staking epoch timeline here:
It takes only minutes to move the funds to the other wallet, but you still get rewards for the high amount in the old wallet for three more epochs. The system cannot automatically redirect them to the new wallet. How should it know that they both belong to the same person?
So, to not miss out on these (perhaps condiderable) rewards, you can wait with deregistering the old wallet until they have arrived.
You can, of course, also decide that you do not care, deregister immediately, move everything to the new wallet and miss out on these rewards.