Download and install Phone Transfer on your computer. After the installation, launch the software and choose "Phone to Phone Transfer" in the main interface.
Step 2 Connect Both Android Phones to PC
Then, in this step, you will be asked to connect your smart phones to the computer with the help of USB cables. Make sure that your old Android is displayed in the left side of the interface and the new one on the right so that you can sync Skype data from old Android to new one. If they are on the wrong place, tap on "Flip" on the top to switch their position.
Note: As we've mentioned above, Android phones running from Android 2.3 to Android 6.0 (including Samsung S6 Edge+/S6 Edge, Galaxy Note 5/4/3, Sony Xperia C4/Z3/Z2, Moto X/ Pro/X/G/E/DROID Turbo), especially the latest Galaxy S7 Edge+/S7 Edge/S7, Sony Xperia Z6/C6, LG G5, HTC One M10/X9, and more works perfectly on this software.
Step 3 Transfer Skype Files between Android Phones/Tablets
In the middle of the interface, you will see various supported files: Contacts, text messages, calendar, call logs, photos, music, videos, apps and app data. Choose "App Data (Root)" and the "App" category will be ticked automatically. After that, click "Start Transfer" at the bottom.
Note: If you have never rooted your Android before, Phone Transfer will ask for temporarily rooting your Android phone and remove it after the end of the transfer process.
That's all you need to do to transfer Skype messages, videos, photos and audios between Android. With Phone Transfer, you just need three simple steps to sync apps data from Android to Android such as WhatsApp photos, Instagram, Duolingo, Facebook messages. Besides, as you can see in the interface, there are other supported data types in this software. You can transfer text files like contacts, call logs, calendar or media files like videos, music, photos, and more.