Outlook Delete email after is saved

The MailItem.Move is in fact a function that return the object that has been moved in the new destination. The old object is kind of "lost", see how to use it (i've commented the deletion part in the whole code ;) )

Set Msg = .Move(FldrDest)
MsgBox Msg.SenderEmailAddress & vbCrLf & Msg.Subject

Full code with some suggestions for improvement (see '--> comments) :

Private WithEvents Items As Outlook.Items

'location to save in.  Can be root drive or mapped network drive.
'-->As it is a constant you can declare it there (and so, use it in the whole module if you want to do other things with it!)
Private Const attPath As String = "C:\"


Private Sub Application_Startup()
    Dim olApp As Outlook.Application
    Dim objNS As Outlook.NameSpace
    Set olApp = Outlook.Application
    Set objNS = olApp.GetNamespace("MAPI")
    Set Items = objNS.GetDefaultFolder(olFolderInbox).Items
End Sub

Private Sub Items_ItemAdd(ByVal item As Object)

On Error GoTo ErrorHandler
    'Only act if it's a MailItem
    If TypeName(item) = "MailItem" Then
        Dim Msg As Outlook.MailItem
        '-->Use directly the parameter and keep it under wraps using "With", it'll improve efficiency
        With item
            'Change variables to match need. Comment or delete any part unnecessary.
            If (.SenderEmailAddress = "[email protected]" _
               Or .Subject = "Smartsheet" _
               Or .Subject = "Defects" _
               ) _
               And .Attachments.Count >= 1 Then


                Dim aAtt As Outlook.Attachment
                '-->Loop through the Attachments' collection
                for each aAtt in item.Attachments
                    '-->You can either use aAtt.DisplayName or aAtt.FileName
                    '-->You can test aAtt.Size or aAtt.Type

                    'save attachment
                    aAtt.SaveAsFile attPath & aAtt.DisplayName
                next aAtt

                'mark as read
                .UnRead = False

                Dim olDestFldr As Outlook.MAPIFolder
                Set FldrDest = Session.Folders("Address1").Folders("Inbox").Folders("Test")
                If .Parent.Name = "Test" And .Parent.Parent.Name = "Inbox" Then
                    'MailItem is already in destination folder
                Else
                    Set Msg = .Move(FldrDest)
                    MsgBox Msg.SenderEmailAddress & vbCrLf & Msg.Subject
                    'Msg.delete
                End If
            End If
        End With 'item
    End If


ProgramExit:
  Exit Sub

ErrorHandler:
  MsgBox Err.number & " - " & Err.Description
  Resume ProgramExit
End Sub