Thank you for your post.
If the USGS topo map was downloaded from the Avenza Map Store, you can transfer it over to your new phone by signing into your Map Store Account on your new iPhone and downloading it from your Download History.
To sign into your Map Store Account, please tap on Account (head/bust icon) available from the Maps List, or Map Store. Once there, please enter your email and password associated with your Map Store account. You will then see your Download History (if you are already signed in, please click the account icon and you will immediately see the download history).
If this is a map that you have imported, this must be re-imported onto your new device from wherever you have the map stored.
Any and all feature data (layers) must be exported to an external storage space e.g. DropBox before you switch phones as this is not information that is carried over with your account.
If this does not work for you or if you have further questions, please fill in the support form at help.avenzamaps.com and we can take a closer look at the issue.
Avenza Systems Inc