I think the one i got is unconditional. it says " please be advised that you have been granted permanent resident alien status as of mm/dd/yyyy. this letter should not be regarded as proof of that status.you are being processed for an alien registration card...if you required proof of your status on order to travel,... you may come to one of our offices for a temporary stamp."
Maybe you can find the answer you need from this letter.
Never know I just want to ask few simple questions get so many people upset there, put it here so you can see it.
Good Luck!