Based on your description, I think you are using Exchange online mailbox.
For Exchange protocol, all actions will be sync to server side then sync to other clients. If you need to use Inbox rule to move emails, I would suggest you use "move a copy to the " " folder" rather than "move it to the " " folder"
Or you could follow this blog to enable POP protocol for your tenant temporarily: Limited Opt Out
Then use command below to enable basic for SMTP service:
Set-TransportConfig -SmtpClientAuthenticationDisabled $False
Wait about 1 hour, then you will use POP protocol for your mailbox again.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.