Yes, you can swap SIM cards between phones. You have to make sure, however,
that if you´re swapping SIMs from different operators that both phones are
SIM unlocked. If you purchased your phone from an operator that subsidized
it they´ll almost always lock the phone so SIMs from other companies can´t
be used.
To unlock a SIM locked phone you need to contact the mobile operator who
provided the phone.
