Asking for a friend: ‘My partner insists she has the right to look through my phone. Will asking her to move in with me reassure her I’m not cheating?’

Q: My partner is insisting they have the right to look through my phone and it makes me feel really uncomfortable. I haven’t done this before with anyone, and I value my privacy. I know she has been cheated on in the past, and I did tell her that I had cheated before. But that was with someone where the relationship was really casual, and we had only gone out for a couple of months. When I first started dating my current partner, she asked me about cheating, and I thought being honest was the best approach as I knew I wanted to make a go of it with her and wanted to be clear. She does have trust issues because of being cheated on before but I don’t want them to cause issues in our relationship. We have had some changes lately with new jobs, and we don’t live together, but I wonder if moving in together will help her feel more secure? We have been together almost a year so I was hoping we would move in together in maybe a year or so, but would it make her happier if I suggested this now? It might reassure her that I am not cheating on her.