Project Client 2010 integration with Sharepoint Task List
First upgrade to at least SP1 the project client because the Sync with task list has been upgraded in SP1
Second, add the field in Backstage - Manage fields.
See:
https://blogs.msdn.com/b/project/archive/2009/10/19/project-2010-introducing-sync-to-sharepoint.aspx
https://www.microsoft.com/project/en-us/sync-sharepoint.aspx
A few important things to notice are:
· Summary tasks are supported in the synchronization
· Most custom fields can be synchronized, and can be added via the Manage Fields dialog (click on Manage Fields button shown on the image above in the Info tab)
· This feature only works with SharePoint Foundation and SharePoint Server 2010
· This feature only works when Project Professional is not connected to the server
You can Import a SharePoint list into Project - see: https://office.microsoft.com/en-us/project-help/use-project-with-sharepoint-HA101805393.aspx
Note: You must have Microsoft SharePoint 2010 Server or Microsoft SharePoint Foundation 2010 to use this feature of Project 2010. In addition, syncing with SharePoint works only in Manually Scheduled task mode (Automatically Scheduled tasks will be changed to Manually Scheduled task mode) and with links that are finish-to-start, with no lag time. Also, if you have resource assignments associated with tasks, for them to be accepted into the SharePoint task list, the resources must be set up in SharePoint as users with the exact same name.
https://blogs.msdn.com/b/project/archive/2009/10/19/project-2010-introducing-sync-to-sharepoint.aspx
Important:
"Sync with Tasks List" is not present in Project Standard 2010 (grayed out) you would need to install the Project Pro 2010
Very interesting link provides differences in the Project Client differences (2003/2007/2010)
https://www.microsoft.com/project/en-us/project-standard-2010-versions.aspx