Nicole Murphy -- Secret Vacation with Ex-NBA Star ... WEEKS Before Breakup Announcement

Nicole Murphy had a secret romantic fling in the Caribbean with former NBA star Jim Jackson in early July -- the exact same time she says she suspected Michael Strahan of cheating on her.

TMZ has obtained photos of Nicole and Jim at the Dorado Beach Ritz-Carlton in Puerto Rico, where they stayed from July 7 through July 10.

You see them in a cabana on the beach ... and they got very snuggly. People at the hotel tell us they were hugging, kissing ... definitely affectionate.

Sources close to the exes tell us ... Nicole had gone to P.R. with some girlfriends, and just happened to run into Jim -- an old friend -- and even though they "hung out" ... it was nothing serious.

We're told Michael knew Nicole was taking the trip with her GFs, but was not aware anything went on with Jackson.

We're told Nicole now says she and Michael were "on a break" when she hooked up with Jackson -- but she did not feel the relationship was over.