Sent G Mails move from Sent Folder to Trash MB Pro

A few days ago every time I send an e mail from my G Mail account it appears in Sent for a few hours or so then moves to Trash. I've been on the phone w Apple Tech Support who can't help because they say it is a Google problem.

I've tried deleting the suspect e mail account in Mail. I've checked the settings in G Mail in the web and there are no Rules, Filters. My settings are IMAP. I have an iPhone and an iPad but do not make changes to mail settings there.

For decades it has worked correctly and I can find the Sent e mails in the send folder in my Mac mail app but suddenly it has stopped working. Nobody can help. Please someone help me.