jquery – SharePoint 2013 REST – Create List Item with Lookup User Field

You have to set Lookups and User Fields using a results object.
If you have a Multi-User Field you should set the value like:

Project_x0020_ManagerId: {"results":(441,448,481)},

If you have a Single-User Field you shet set value like:

Project_x0020_ManagerId: {"results":441}

In your case this code should do the trick:

var data = {
__metadata: { 'type': 'SP.Data.ProjectsListItem' },
Title: '' + name + '',
Start_x0020_Date: new Date(start).toISOString(),
End_x0020_Date: new Date(end).toISOString(),
Project_x0020_ManagerId: {"results":441},
Additional_x0020_Details: note
};
$.ajax({
    url: siteURL + "/_api/web/lists/getbytitle('Projects')/items",
    method: "POST",
    contentType: 'application/json;odata=verbose',
    data: JSON.stringify(data),
    headers: {
        "Accept": "application/json;odata=verbose",
        "X-RequestDigest": $("#__REQUESTDIGEST").val()
    },
    success: function(data) {
        alert('Item added successfully');
    },
    error: function(error) {
        alert(JSON.stringify(data));
    }
});