That picture doesn't show a shield - it shows a PCB. (In Arduino terminology, a 'shield' is a PCB with headers that align with the headers on an Arduino, which is designed to mount on top of the Arduino.)
It looks to me as if that device is designed to use 5-wire RS232 and your RS232-TTL converter provides 3-wire RS232.
I suppose it's possible that you could just pull the RTS (7) low and see whether the PMD570 will receive data. It ought to respond by setting CTS ( 8 ) high, which in your case would make DSR (6) and DTR (4) high - those aren't mentioned in the description of the PMD570 and perhaps it doesn't use them. The main issue I see is that according to your diagram none of these control signals are taken back to the logic level interface so the Arduino doesn't have any way to know whether the PMD570 is ready to receive data. I suppose you could just pull RTS (7) to ground and see if it makes any difference? It would be worth check what the PMD570 does to CTS ( 8 ) in response - hopefully that would confirm that you've identified the connections correctly and I'm reading the description properly.