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*Leave it to TMZ to come up with the grainy pictures purporting to show Nicole Murphy having an alleged romantic encounter in Puerto Rico last month – just weeks before she announced her breakup with fiancé Michael Strahan.

The website reports:

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.

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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.

Still … it’s interesting … she’s accusing Michael of cheating but she was clearly playing the field.

Jim Jackson, seen here playing for the Los Angeles Lakers in 2006

Jim Jackson, seen here playing for the Los Angeles Lakers in 2006

Jim Jackson, 43, played for 14 seasons in the NBA, on 12 different teams. He is currently an analyst on the Big Ten Network.