Copying rows based on criteria

Is this what your wanting?

Option Explicit
Private Sub CommandButton1_Click()
 Dim shName As String, cFind As Range
 Dim sh As Worksheet, lr As Long, c As Range
 
 Set sh = Sheets("MasterSheet")
 lr = sh.Cells(Rows.Count, 1).End(xlUp).Row
 For Each c In sh.Range("a2:a" & lr)
    Select Case c.Value
        Case Is = "AAAA"
            shName = "Centre1"
        Case Is = "BBBB"
            shName = "Centre2"
        Case Is = "XXXX"
            shName = "Centre3"
        Case Is = "YYYY"
            shName = "Centre4"
        Case Is = "ZZZZ"
            shName = "Centre5"
    End Select
    With Worksheets(shName).Columns(1)
        Set cFind = .Find(c.Offset(, 1).Value, LookIn:=xlValues, LookAt:=xlWhole)
        If cFind Is Nothing Then
            .Cells(Rows.Count, 1).End(xlUp).Offset(1).Resize(, 3).Value = _
                c.Offset(, 1).Resize(, 3).Value
        End If
    End With
 Next
End Sub