Hi Check the rx and tx and gnd pins on the chip are correctly marked to the marking on the board, also a good test to do is connect tx and rx together on the ttl side of the board and use a terminal program it should echo what you type if it does not do the same with the rs232 level,
As I had a problem with the same chip from china, the board had a max3232 and a DB9 plug mounted on the board and a Header for rx,tx,gnd, 3.3-5v, I was trying to program a Tait radio but could not connect, then I linked tx and rx together and tested the chip in windows terminal and the chip was working,so I put a scope on the tx pin,and got nothing when I sent text, put the scope on the rx pin when I sent text and got the TTL levels, so the problem was the screen printing on the pcb was wrong the rx pin was maked as the tx pin, and tx was rx,
so just look up the data sheet on the MAX3232 chip,
Dave