A free app for Android, by ZamenPlay.

Contacts Backup & Transfer App lets you back up, manage, transfer, recover, and copy your contacts easier and faster. With this app, you can effortlessly import,  export, and even share any of your contacts.

The app has different unique and useful features to offer such as Smart Contact Transfer with Smart Switch, Super Backup to Backup Contacts, Restore Contacts in Phonebook App, Transfer Contact with Contact Mover, Manage Contacts with Contact Manager, Secure Cloud Storage of Contact Mover, and Safe Backup Assistant.

Once installed, just log in to the contact transfer app using the same number or email right after the authentication process. After that, you can now manage, restore, copy, transfer, and handle everything on your contacts.