In new legal docs obtained by TMZ, Weinstein's lawyers -- Jennifer Bonjean and Michael Freedman -- are officially appealing his 2022 rape conviction in L.A. ... claiming prosecutors relied on false testimony to advance a flawed narrative from one of his accusers.

They also went after the prosecution for allegedly introducing prejudicial information from previously uncharged alleged sex offenses unrelated to the case -- which they say unfairly swayed the jury against Weinstein.

His lawyers state HW's constitutional rights were a "casualty" in the trial, noting he's entitled to a retrial where his rights are "safeguarded, where he is permitted to present evidence of his innocence, and where his conduct is on trial - not his character."

You'll recall ... Weinstein's lawyers made similar points while fighting for his appeal in NY. Remember, Weinstein's team claimed he was deprived of a fair and impartial jury trial, blaming sensational media coverage for influencing the jury.

His NY appeal docs also called out one specific juror, who they said lied about writing a book about older men preying upon younger women.

Ultimately, Weinstein's appeal was successful ... with the appeals court tossing out the conviction as they felt too many witnesses were allowed to testify about uncharged alleged prior sexual misconduct. Of course, he's going on trial anew in New York -- with prosecutors seeking another bite at the apple.

Weinstein was found guilty of one count of rape and two counts of sexual assault in his Los Angeles trial ... but was acquitted of a count of sexual battery.