I rated 5 bc "Android Messages" app definitely filled the gap between iPhone iMessages phone sync experience and my switch to Android. But by the developer's own words, this app is no longer working/supported but a simple alternative is recommended:
https://www.flotato.com/
Not so straightforward (read: App-specific) but easy nonetheless. Install the free Flotato, browse to the "Google Messages" app you want to install, follow the directions. (scan the QR from within the official Messages app on your Android phone)