Transferring a specific app from one Android device to another
You'll need to do a full backup of that app, i.e. including its data. That usually requires root, but there are some solutions for this specific case to make it work without root – see Full Backup of non-rooted devices. The two candidates you should look at:


adb backup -f &lt;appname&gt;.backup -apk &lt;package_name&gt;
Helium Backup (an app which does this on-device, but will need to be initialized via ADB)


Basically, there's no way around adb for this. For details, see the linked question with its answers, and our adb tag-wiki.

Note: As Death Mask Salesman correctly pointed out, apps can opt out of ADB backups (developers can include a flag in their apps' Manifests advising the system to not permit ADB to back it up). So if your app falls into that category: bad luck without root.