It’s been a while since Google informed Translator app users about saving history to Google Account. Now the function is there. In fact, it should probably take two years for Google to actually implement the announcement at the time for users. Now the translator app saves your history in your Google account, which should therefore also be directly available on all your other devices.
Google Translate stores history online
You can save your Google Translate history to find the meaning of words or phrases you are translating. Your saved translations are synced across all your devices.
The Translator app syncs your history from your device to the cloud. When you are logged in, your translations are automatically saved to the cloud. You can manage your saved history in My Activity.
Important: If you don’t want to use cloud history in the app, you’ll need to sign out of your account. After you sign out, you can only view the history on the device.
This feature requires Web & App Activity to be enabled for your Google account. You can see all the histories there and therefore also that of your translator app.