Froggle Jump for Android
The same game you play in the browser, on your phone. Free — there is nothing to buy on this page.
Installing it
This is a direct download rather than a Play Store listing, so Android will ask you to confirm before it installs. Open the downloaded file and allow installing from your browser when prompted — the setting is usually called Install unknown apps.
Your account and stars
Sign in with the same Google account and your stars, unlocks and best score are already there — it is one account across the browser extension and the phone.