Scan all your email devices to remove password capturing viruses, trojans and other malware before changing any password. Also to delete any Rules (Filter rules) spying on your mail messages by copying or diverting mail from your Inbox.
In addition, as soon as you get access to a newly migrated mailbox there is an additional Security option to forcibly sign out any unrecognised devices.
Via the main settings cog icon top right, select the All settings menu item, select Security and Sign out any unrecognised device or select Sign out all devices and confirm the sign out of all except the one you're currently using.
