espec MC-811P don't connect with PC via RS 232 rs 485 converter

Hello all,

I'm having some difficulties setting up and RS485 link with a climate control chamber from ESPEC.
It is a MC-811P climate chamber. The climate chamber has two male DB9 connectors on the outside, apparently used for linking multiple RS485 chambers together.

The pinout of the DB9 RS485 intrerface connector is:
1: SD+ Transmission data (A) Connected
2: SD- Transmission data (B) Connected
3: RD+ Reception data (A) Connected
4: RD- Reception data (B) Connected
5: GND Ground Connected
6: GND Ground Connected
7: NC (Not connected) Not connected
8: NC (Not connected) Not connected
9: NC (Not connected) Not connected

I have bought a RS-232-to-485 interface converter . This converter also has a male DB9 interface but the pinout is different.
1: Data -
2: Data+
3: -
4: -
5: GND
6: -
7: -
8: -
9: -

So - the pinouts do not match and I see different signal names on both interfaces.

Am I correct in assuming that I should only make the following connections:

Converter 485 to ESPEC climate chamber
1 2, 4
2 1,3
3 not connected
4 not connected
5 5,6
6 not connected
7 not connected
8 not connected
9 not connected

Are there some special things I need to do to get this setup to work?
I'm using LabVIEW as my programming language to try and control the climate chamber.
I'm especially not sure how I need to set up to get everything working...
In the ESPEC documentation I could find that the communication system used is "Synchronized modulation (four-wire, half duplexing)".