Jealousy can be a hard emotion for people to admit (even to themselves) that they are experiencing. Jealousy, envy, pride etc are often regarded to be terrible, horrible emotions that nice and kind and decent and respectable people simply don't feel. I think that all of these feelings are normal and that everyone experiences them at times, but they can surely be hard emotions to face up to because of the way they tend to be viewed in society.

Sometimes jealousy can arise because a person feels left out of something. They perceive that other people have something that they need (emotionally) and they feel deficient in some way and wish they had that for themselves. It might be that this person saw that you both experienced a special closeness and a bond and that stealing the item wasn't so much an attempt to destroy the bond that you had but arose more from a desire for her to feel part of that bond, too. It could have arisen out of lonliness or something like that.

Sometimes empathizing with the person can involve trying to place ourselves in their shoes. To be able to forgive someone often means adopting a charitable take on their rationale for doing what they did so that we can place ourselves in their position and feel compassion for them. I'm not saying that you should forget what has happened (or let her back into your home). But maybe reflecting on times when others have had something that you wanted (emotionally) might have you placed to forgive what this person has done.

Perhaps...

Though I guess you won't know why she did it until you ask her. And of course she might not know why she did it (she might have adopted a view of herself where she is a horrible jealous person and be afraid that maybe she is so she might not know why she stole it). If you could talk to her about it in a way that is seeking understanding instead of condemnation she might be able to tell you why... But it might be that she is so afraid of herself that no matter how caring and compassionate you are in asking she simply won't be able to give you a satisfactory answer.