Transition current Android phone and legacy iPhone to new iPhone

Try this...

iPhone to iPhone, there are three ways,

1. Quick Transfer --> Use QuickStart to transfer data to a new iPhone, iPad or iPod ...
2. Restore from iCloud Backup --> Restore or set up your device from an iCloud backup - Apple ...
3. Restore from iTunes backup --> Restore your iPhone, iPad, or iPod touch in iTunes on PC ...

Android to iPhone

1. Do not Use --> Move from Android to iPhone, iPad, or iPod touch - Apple ...
2. You probably have already set up your device using either of the above three options, then you can still transfer these data from your Android device to iPhone
   1. Photos & Videos --> Upload to iCloud Photos using the same Apple ID that you have used on your iPhone. After upload, enable iCloud Photos on your iPhone. That's it.
   2. Contacts --> Contacts are not stored on an iPhone nor on SIM, they are synced to  Google, iCloud, AOL, Exchange, Outlook, Yahoo or any Other. Upload all your contacts to any of the above email client-server.
   3. Notes, Reminders, Calendars --> You may sync all these from any of the email accounts that you have. they are synced to  Google, iCloud, AOL, Exchange, Outlook, Yahoo or any Other. Upload all your data to any of the above email client-server.
   4. Any Specific Files --> Upload to Cloud Drives (iCloud Drive, Google Drive, OneDrive, DropBox, Flickr, box, AmazonDrive, Adobe Creative Cloud and Use Files app on iPhone
   5. Apps --> In any way they have to be redownloaded using the App Store.
3. WhatsApp --> My experience says you can't transfer because on Android, WhatsApp, chat history is not stored on iCloud, on iOS it is.
   1. That may be possible with third-party software. Warning!; WhatsApp data through third-party software has the risk of data being compromised. Because the data will be churned through third-party servers, which may or may not be encrypted. Be judicious while selecting the software and taking this call.
   2. Having said that, WhatsApp is not an Apple product. Contact the app developer here --> App Support or WhatsApp FAQ or Restoring your chat history - WhatsApp FAQ
4. Shazam Account --> Access your Shazams on all your devices or online - Apple ...

You have the right idea. First, set up the new phone from the Android.

Then, on the 4S go to Settings[your name]/iCloud and turn on switches for anything you want to sync to the new phone, which can include Messages. You would have to sync music from iTunes on your computer unless all of your music was purchased from iTunes. In that case you can just download it from the iTunes store.

You can do one or the other, but not both.