Fill a MsAccess table using a DataTable

Question

I have to transfer a whole datatable, OriginaDataTable, into another Ms Access table with the same structure. I've tryied with DataAdapter but something went wrong as no rows are written.

using (OleDbDataAdapter a = new OleDbDataAdapter("SELECT * FROM [TableToFill]", cnn))
{
    a.Fill(OriginaDataTable);
}

I'm missing something?