Anyone can transfer their data from Basecamp to activeCollab. All you need is a valid activeCollab license and a copy of the data on your Basecamp account.
To start the migration you should begin by logging in to your account on the activeCollab website. If you haven't bought activeCollab yet you will automatically receive an account upon purchasing a licence. Once your account is set-up, please make sure you keep the login details in a safe place, because you will need to use them later on the Migration Center page to start the transfer process.
You will also need to export the Basecamp XML file before you start the migration process. This is something that only the Basecamp account owner can provide, so if you're not the account owner just get in touch with the person who is and let them know what you need - the Basecamp XML file and the Basecamp account owner's login details. Since the account owner is authorized to do everything, it would be the best to go trough a data migration process in this way.
Now that you have your activeCollab license and Basecamp XML file, you can start the data transfer.