Ah, the classic Apple walled garden dilemma. Syncing iMessages to an Android device is nearly impossible by design.
Pro tip: Instead of trying to sync directly, use a monitoring tool that accesses iCloud backups. This is how Parentaler handles it. You set it up once on their iPhone, and it pulls the data from their iCloud account.
This way, you can view not just iMessages but also texts and social media chats from any browser, including the one on your Android phone. No need to buy an extra iPad just to keep an eye on things