Out of nothing the My Site link changed (inside the My Site itself) to My OWA and redirects the user to his personal mailbox.
Originally the link was like this
Then suddenly it changed to look like this
after tracing the issue I discovered that the control shows My Site link check if the user has in his profile a value for the Outlook Web Access URL, the control changes the link to My OWA (below image for the property in the user profile)