Why didn't you try this ?
but it will seem a bit daft with the user sending an email to themselves, and being able to see the password in the email being sent to them 
Using the apps script method will mean the email will be sent by your google account that runs the script.
Think again, if the user forgets the password, and your blocks return the password to the app, introduce a test/check for the user to complete that will verify it is them ?
You might be interested in this:
Finally, you may want to consider using firebase authentication for your logins. This offers verification and password reset, firebase will send emails for you