SAT1142 is the name of a setup code that could be added to the remote via a JP1 cable.

Without a JP1 cable and assuming Edmund is right (I haven't lookep up anything about the DSX 5350 to check that) you could only control it by learning every code from the orriginal remote into the 7800 (It is a learning remote). But it doesn't have capacity for a lot of learned signals, so you might need to pick just the important ones.

Even with a JP1 cable you need a "header" to connect the cable to the 7800 (most JP1 capable remotes come with that built in, but the 7800 doesn't). With some difficulty you can use the header as an adapter on the end of the cable and not need to take apart the 7800. Most JP1 users prefer to take the 7800 apart and solder in the header, so the cable is then easy to use.