yes but....he can't have the number on two phones at once so he'll either have to have his gift before christmas or get his number ported after christmas. Getting a number ported between christmas and new year is a nightmare. Is he staying with the same provider?
If the new phone is either unlocked or on the same network as the existing one, then he will be able to simply put his old SIM card into his new phone. Is it PAYG?
CheekyChops is correct but be aware that there at least 3 types of SIM (SIM, Micro and Nano) so even if the provider is the same but the phones use different SIM types then you can't just move the SIM between devices so the service provider will need to make the new SIM active with the old number.