Sources with direct knowledge tell TMZ ... Ben and J Lo were in very regular contact by email starting in early February when she flew to the Caribbean to begin filming "Shotgun Wedding." We're told the tone of the emails wasn't just friendly ... but more loving and longing for Jen.

For instance, after seeing pics of Jennifer in the D.R., he wrote to tell her how beautiful she looked, and how much he wished he could be down there with her. Of course, he was busy at the time in Boston, shooting "The Tender Bar" with George Clooney -- and she was still engaged to Alex Rodriguez.

Our sources say the emails also referenced J Lo's love for Ben's writing, and included a line about him being able to "own her heart" with his pen.

We're told they continued emailing each other, back and forth, for the duration of J Lo's shoot ... which wrapped in late April.

As far as our sources know, there was no physical contact or rendezvous between them during this time, but the emails do add context to how they seemingly got together so quickly.

Remember, they were together in L.A. -- very publicly -- on the first weekend in May ... just 2 weeks after Jen and A-Rod called off their engagement.

Folks in Ben and Jennifer's world said they had always maintained a friendship since splitting up in 2004. However, as we first told you, they were together again in Montana this past weekend.

One more clue the exes have been in close contact for some time came with InStyle Magazine's recent J Lo cover story. It included a quote from Ben gushing about his ex-fiancee, saying in part ... "She has great talent, but she has also worked very hard for her success, and I’m so happy for her that she seems, at long last, to be getting the credit she deserves."

That story did not include a quote from Jen's then-fiance, A-Rod.