I solved this problem and I will answer here if it can help someone. The problem is that the RFID module crosses RX and TX (DTE device) as can be seen from the scheme in my previous post. This makes that TX from the RFID module is connected to T1OUT and RX to R2IN in pmod rs232 (see this). The solution was to swap RX and TX in the RS232 side, i.e., before connecting to the pmod rs232.
It took me two days full time to figure this out...bear always in mind that this pmod rs232 module is configured in DCE mode!