SharePoint 2013 - User cannot edit documents on their computer, log on to mine and they can (they have correct permissions)?

I have a user who is trying to access MS Office 2013 files in SharePoint, this user has all the permissions necessary to edit the documents but when they open the files it says read only and when they try to save the document it asks them to save it to their computer.

When they log on using my computer they are able to go on SharePoint and access, edit and save these documents.

When I log onto their computer I get the same issue they have where I cannot edit and save documents off SharePoint.

I Reinstalled Microsoft office and Internet explorer 11 on their computer but this has not resolved the issue.

I am not sure what else to do.
Any help will be greatly appreciated.