You can have the function call itself, as it appears it should be opening thunderbird via Shell. I highly recommend you get the error number and what occurred when this doesn't work though.
Public Function fSendThunderbird()
on error goto errsend
Dim strCommand As String
Dim strTo as string, strCC As String
Dim strSubject As String
Dim strBody As String
Dim strFilePath As String
strTo = "myemail@.cie.com"
strCC = "myemail@.cie.com"
strSubject = ThisWorkbook.Name & " " & Format(Range("E3").Value, "mmmm yyyy")
strFilePath = Application.ActiveWorkbook.FullName
strBody = "Hello"
strCommand = "C:\Program Files (x86)\Mozilla Thunderbird\thunderbird"
strCommand = strCommand & " -compose " & "to=" & strTo & "," & "cc=" & strCC & "," & _
"subject=" & strSubject & "," & "attachment=" & strFilePath
Call Shell(strCommand, vbNormalFocus)
End Function
Exit Function
errsend:
'Highly recommend handling errors here. 49999 is just an example
If err.No = 49999 then
'fatal error
Call KillThunderbird
else
Call fSendThunderbird()
end if
End Function
Sub KillThunderBird
Dim oServ As Object
Dim cProc As Variant
Dim oProc As Object
Set oServ = GetObject("winmgmts:")
Set cProc = oServ.ExecQuery("Select * from Win32_Process")
For Each oProc In cProc
'Rename THUNDERBIRD to match what it comes up in as in Task Manager Processes
If oProc.Name = "THUNDERBIRD.EXE" Then
errReturnCode = oProc.Terminate()
End If
Next oProc
End Sub