I assume you use the Google Authenticator as 2FA feature.
In that case, there is no link between your account and mobile phone number / SIM / etc... The only piece of information to regenerate 2FA access to your account is the secret that was provided when you first activated 2FA, either as a string of digits & letters or as a QR code. With it, you can recreate the same 2FA codes on any device, regardless of whether it is networked or not.
Google Auth 2FA basically works by hashing a combination of the aforementioned 2FA-secret with the current time. If you have the secret and the time on your device is reasonably accurate, the codes generated will be valid.
Thanks for the information, I understand now.
I don't remember a code when I installed the app, I do not have one recorded.
You don't get the code when you install the app, you get it when you activate it on a website, e.g. Bitstamp. When you enable GAuth, you're shown a QR code to scan with your phone and a alphanumeric code that you can type in. It is important to write down this alphanumeric code somewhere (and/or make a screenshot of the QR code), because if you lose access to your phone, you'll need that code to restore access on a new phone.
If you haven't written down the code when you activated 2FA, your best course of action is to disable 2FA and then immediately reenable it, which gives you a new code, and then writing that down.
Most websites have some recovery-process for those that have lost access to their 2FA device (and have no backup of the code), but it regularly involves a waiting period or other hassles. Much better to just create a backup.
