We've verified Hernandez sent the note from the Souza-Baranowski Correctional Center on Dec. 10th ... to a female pen pal he'd exchanged letters with in the past.
Aaron -- who's serving a life sentence for murder -- begins his letter on the attack, ripping the woman for criticizing him in her last correspondence ... and suggesting ways she should kill herself.
"Tie a cinderblock to your ankles and jump in a deep body of water," Hernandez writes.
He then suggests, "Buy the most powerful firecracker in the world that's possible to buy, tie it to your face with duct tape, light it and wait for your head to explode."
Hernandez then changes subjects and goes off about his former team -- saying:
"I have a TV in my cell! And yes I still root for my squad and still love all the ones I loved.
The closest I was with was probably Brady and whom I love to death and always will and only hope the best for them. But was cool with Julez, Branch (I f**ked with and got mad love for) and 'the BEST TE ever to walk on a football field' Gronk!"
Hernandez moves from love to hate ... ripping into "fake ass non loyal Kraft who told me he loved me every time he seen me but obviously shows his word ain't sh*t."
Hernandez says no matter what happens to him in prison, he'll continue to support his boys.
"I watch every game faithfully cheering them on and always will cuz I have love for so many of them!"