Yes, you can, if you have the necessary login information. A private proxy is transferable, so to speak. This is one of the reasons that people tend to want to use a private proxy for. It is easy to use and safe regardless of the computer you are using it for. As mentioned, you have to know the username and the password for your private proxy to work and that is all. There are a lot of people that use private proxy just to make sure that they have safe access to their resources everywhere, so it might be the best option for you as well.