A couple of cautions.
First, make sure the transmitter can handle the total load in the circuit. You will have 250 Ohm at the recorder, probably 250 Ohms at the PLC, and some resistance in the loop wiring. Your transmitter is probably rated for a maximum load of around 600 Ohms, so you are probably OK, but you need to check this. If you have any other devices in the loop, like a local indicator or such, or if your transmitter supply voltage is low, or if your transmitter has a low load rating, you will be in trouble.
Second, most PLCs have one side of the 4-20 mA input tied to ground. Many chart recorders do the same thing. This creates what is called a ground loop - only the first device gets the current signal, which goes to ground instead of to the second device in the loop. If this is the case I suggest you put an isolated signal conditioner in the loop at the chart recorder and ahead of the PLC. The conditioner will be low impedence (verify) and can provide a 1-5 VDC for the recorder and let the current signal continue through the loop to the PLC.