In order for you to say, “S03 it does the sustain properly” means it works sustain ON when pressed, Sustain OFF when released. That is proper for a Foot Switch set to do Sustain (cc64)
If the sustain does not go OFF when you pick up your foot, then it is not working properly.

Possible causes for it not work properly:
The pedal is not plugged all the way into the dedicated “Foot Switch” jack on the back panel
The Foot Pedal is set not to send FSTxCtlNo = 64 (Foot Switch Transmit Control Change #64)

See page 46 of your Owner’s Manual
An optional Yamaha FC4 or FC5 Foot Switch connected to the rear panel FOOT SWITCH jack (page 10) can be assigned to a range of parameters. This is designed for switch-type (on/off) controls such as incrementing/decrementing Voice or Multi numbers, and cannot be used for continuous control of a parameter. The default factory setting for this is to control sustain (FSTxCtlNo = 64).

If you are connecting FC4 to S03, the sustain pedal can cause problems. The problem is that there is no switch on the sustain pedal and it needs a special cable to enable it. mapquest directions

You need to connect a cable from the sustain pedal socket on FC4, to the Sustain socket on S03. There is also an optional footswitch available which enables you to turn off the sustain automatically when you take your foot off it.