welcome to the forum.
copy below code to a standard module (or Geplande afspraken's code module) and assign it to the button Klantenlijst in sheet Geplande afspraken (cell F3)
Sub vbax_63629_cut_paste()
Dim rww As Long, lbr As Long
With Worksheets("Afspraak geschiedenis")
lbr = .Columns("B").Find("*", .Cells(1, 2), xlValues, xlPart, xlByRows, xlPrevious).Offset(1).Row
End With
rww = ActiveCell.Row
With Range("B" & rww & ":F" & rww)
.Copy
Worksheets("Afspraak geschiedenis").Range("B" & lbr).PasteSpecial xlPasteValues 'in order to keep destination cells' formats
.ClearContents 'in order to keep source cells' formats
End With
End Sub
if you want to run it without using a button, do it after selecting the sheet Geplande afspraken.