Often the problem can be resolved after you restart your Smartphone after receiving the error message.
How to Fix com.google.process.gapps has stopped unfortunately:
Delete the Google Play Store Cache, if the message occurs again. To remove the Google Play Store cache, open the settings on the Android device. Now Move to the application manager and it will display "All" apps. Here you can find the Play Store After selecting you can clear the cache and data. If the message appears again, uninstall all updates.
Moreover, the problem may be caused by a faulty synchronization of the Android device with the Google account. If the above solutions does not work, open the device settings again and calling the section "Accounts." Select the Google account and click "Remove account". Once the account has been deleted from the device, you can add a new account by selecting "Add Account" in the lower right corner of the same section. After re-establishment of the Google account, an error "com.google.process.gapps" should no longer occur.