Harvey Weinstein Set to Be Retried Criminally After Conviction Overturned

12:29 PM PT -- Harvey Weinstein's rep, Juda Engelmayer, tells TMZ ... their legal team is curious to see if prosecutors can whip up the right witnesses to do this again. He says he believes one of the original complainants perjured herself already ... so they don't think the D.A. has a case.

If they do wanna run it back, though, Engelmayer says Weinstein is up for the challenge ... despite his health issues. He says HW has a renewed glimmer of hope and restored vigor.

Harvey Weinstein is going to be put through the wringer again in criminal court out in New York -- because prosecutors say they're retrying him ... which will happen later this year.

Prosecutors had already signaled they were prepared to take another shot at convicting Weinstein -- and on Wednesday, they made it official in court ... telling a judge they're seeking another trial, which they're hoping to get underway in September.

Specifically ... the court cleared the schedule for Weinstein to be tried sometime after Labor Day -- so right after Sep. 2 ... meaning HW has a few months to prepare with his lawyers.

Weinstein showed up in person for this news ... he was wearing a suit -- and his attorneys touched on his failing health ... noting it was a big deal he was able to be there in the flesh. Considering he was hospitalized just last week, we suppose that's technically right.

No word on how Weinstein and co. took the fact there'll be another trial -- but we know he and his team have insisted on his innocence from the beginning.

While he scored a legal victory in having his original 2020 conviction overturned last week -- Weinstein will now need to mount a defense anew ... as prosecutors tweak their approach and go for another bite at the apple.

Remember ... the appeals court tossed the conviction because they felt too many other witnesses were allowed to be called to speak on things HW wasn't on trial for.

Since the Manhattan D.A.'s Office is dead set on going for round 2, that presumably means the 2 women who were their star witnesses last time are going to be front and center again.