Ultimately, this is an opinion question. Your main job is to make sure that your letter stays within character for Elizabeth. I am uncertain as to when Elizabeth might be writing this letter to John. Is it before or after she visits him in prison? I don't feel that the answer to that question is super important. What's important is that she does visit John. That's what I would use for inspiration for your letter to John. I would have Elizabeth write the letter before she visits John in prison. I might even suggest that she writes the letter in lieu of going to see John.
It is during Act 4 that Elizabeth visits John in prison. Have her letter mimic the information that she and John discuss. First, write about how the pregnancy is going. This will not be John and Elizabeth's first child, so be sure to update John on how his sons are doing.
"They're well. Rebecca's Samuel keeps them."
Next, write about Giles Corey. Tell John about how Giles refused to confess anything even while being pressed. Be sure to tell John that Giles died during the torture. I would add in that Corey's wife still refuses to confess anything, and that is also true of Rebecca Nurse.
At this point in your letter, you could go a couple of different directions. You could write out your goodbye to John because you know that he is going to die. You could tell him what you love about him, and you could emphasize that he is going to die as a good, Christian man. On the other hand, your letter might beg John to confess. During Elizabeth's visit to John in the prison, she does at one point admit that she would like him home.
"I want you living, John. That's sure."
I believe that Elizabeth might encourage John to confess the lie to save his life. She previously showed her willingness to lie in order to protect John when she lied to the court about his adultery. I don't believe that having Elizabeth encourage John to protect his own life by confessing a lie is out of character for her. Additionally, Elizabeth does tell John that other community members confessed in order to save their lives. I believe that she tells John this information so that he doesn't feel he would be the only person to confess.
"There be a hundred or more, they say. Goody Ballard is one; Isaiah Goodkind is one. There be many."
Regardless of which direction you choose to take at the end of your letter, it needs to be clear that you both love and support John and his decision.