Copy multiple cells (not in range) from one sheet to another sheet

To keep it simple and for easier debugging, use helper cells.

In an unused row, row 99 for example, link to your four source cells (A99=A10, B99=F2, C99=F3, D99=F34). Then the macro is straightforward. Hide row 99 to keep it clean.

This VBA Macro will do it:

Public Sub resume_invoice()
    Dim wkb As Workbook
    Dim wks, wks1 As Worksheet
    Set wkb = ThisWorkbook
    Set wks = wkb.Sheets(1)
    Set wks1 = wkb.Sheets(2)
    use_row = wks1.Cells(wks1.Rows.Count, "A").End(xlUp).Row
    use_row = use_row + 1
    If wks.Cells(3, 6) <> wks1.Cells(use_row - 1, 3) Then
        wks1.Cells(use_row, 1) = wks.Cells(10, 1)
        wks1.Cells(use_row, 2) = wks.Cells(2, 6)
        wks1.Cells(use_row, 3) = wks.Cells(3, 6)
        wks1.Cells(use_row, 4) = wks.Cells(34, 6)
        Set wkb = Nothing
        Set wks = Nothing
        Set wks1 = Nothing
    End If
End Sub

Go to macro / VBA, under ThisWorkbook insert a module and paste the code.

To make it easy to use you can assign a button to execute it.