Transfer authenticator to new phone without old phone

You can't transfer Google Authenticator to a new phone without the old phone, but you can switch your Authenticator key to a new phone by logging into the 2-step verification section of your account settings and clicking Change authenticator app.

Sign in using the Google Account whose codes you want to transfer. Scroll down the 2 Step Verification Page, then click on Change Phone on the Authenticator App Tab. Select the OS version of your device, either Android or iPhone. Click on Next.

If you've lost access to your primary phone, you can verify it's you with: Another phone signed in to your Google Account. Another phone number you've added in the 2-Step Verification section of your Google Account.