//記錄修改前A表的A1
procedure TForm1.Table1BeforeEdit(DataSet: TDataSet);
begin
  old_A1 := Dataset.FieldByName('A1').AsString;
end;
//A表存完檔後更新B表
procedure TForm1.Table1AfterPost(DataSet: TDataSet);
var
  qry: TQuery;
begin
  qry := TQuery.Create(nil);
  with qry do
  try
    DatabaseName := '給Alias Name'
    SQL.Clear;
    SQL.Add('Update B Set A1 = :new_A1 Where A1 = :old_A1');
    ParamByName('new_A1').AsString := Dataset.FieldByName('A1').AsString;
    ParamByName('old_A1').AsString := old_A1;
    ExecSQL;
  finally
    FreeAndNil(qry);
  end;
end;

Create Trigger UpdateB on A 
  For UPDATE
  As
    UPDATE A
    SET A1 = I.A1
    FROM A A,inserted I,deleted D  
    WHERE A.A1 = D.A1 AND D.A1 <> I.A1