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.
