Not to be critical, but actually while this will work, it is *NOT* the best way.
Here's why: The keying transistor already has to engergize the relay coil. Hard work. But having to charge up a 1000uf capacitor is also hard work. If you really want to get technical you could check out the time constant of the circuit, but really, this is a band aid approach.
Now, let's also hope that whoever built the amplifier put a doide across the relay contacts to prevent a spike as the amplifier is unkeyed. The effect of the magnet coming back at the coil can cause a pulse that can also take out the keying transistor.
If you really want to do this correctly, you should add the delay to the base of the keying transistor. You will need a small value electrolytic. Polarity is dependant upon what transistor is used. (PNP or NPN)
Usually about 22mf, but in reality it all depends upon the keying transistor used. This causes the keying transistor to remain in an "ON" state after the current has gone away from the rectifiers / diodes that are sampling the RF. It can also help prolong the life of the keying circuit as well, as some are designed poorly, and the keying transistor is actling like a switch, turning on and off quicker then the eye can blink, but obviously too fast for it to affect the relay.