Yes, you can. We recommend you open an account with Dropbox or a similar service. When you have the account, you can share folders between your laptop, PC, mobile phone, or other device and store your CNC Simulator files on it. This also means that your files are automatically backed up.
Another option that has been added to the simulator is the built-in cloud service. You can Save and Load files to the CNC Simulator Cloud using the File menu.