No one wants to mislead on LinkedIn. Well, maybe some do. Second message to me asking my help in 2 weeks:
How do you get an ex-employee to drop listing he/she is currently employed on their LinkedIn profile?
First try asking them professionally and nicely via LinkedIn or via email to correct their status as having left your company. Give them some time to react to this. You’ll likely know what the circumstances are and how long to wait.
If that fails, LinkedIn has a process to follow. It’s an online form to have them investigate your claim and push the offender to action. As the form says,
LinkedIn relies on the integrity of its members in providing true and accurate information in their accounts, and does not control or vet user-generated content for accuracy. Submitting a Notice will not necessarily result in the removal of the account or information. LinkedIn and/or SlideShare will use this Notice, including your contact information, to investigate your claim.
That should get their attention!
I had such as situation twice in past years. Both were resolved. Yours will be too.