Question: I have a 433.92 MHz gate opener remote that I would like to be able to control from my phone. In order to do this I have soldered a relay to one of its buttons, which I already have means to trigger through Home Assistant.

Sadly, the range isn't good enough to reliably reach the receiver. I have thought about somehow adding an extra antenna to it to increase the distance it can transmit.

I suspect that the area I marked with purple on this image is the current antenna: [![HR TECH3 Remote circuit board](https://i.stack.imgur.com/fnSL0.jpg)](https://i.stack.imgur.com/fnSL0.jpg)

Is my assumption correct, and is it worth trying to extend the range by soldering some extra copper wire to it? In case it's worth a try, is my research so far correct, that suggests that I should be using a copper wire of length ~173mm?

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*Edit #1:* I have identified the remote as being an HR TECH3: <https://www.hrmatic.es/producto/hr-tech3-remote-control/>

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*Edit #2:* I finally went with the [idea of @Chu](https://electronics.stackexchange.com/a/626879/206656) and built a passive reflector. So far it seems to work very well! I wish I could accept it as correct too, but I guess that strictly speaking [@Marcus Müller's answer](https://electronics.stackexchange.com/a/626879/206656) addresses the original question more directly.

[![passive reflector](https://i.stack.imgur.com/M1NAe.jpg)](https://i.stack.imgur.com/M1NAe.jpg)

Answer: 
No.

You can build a *better antenna*, which would mostly mean that in exchance for needing to point more exactly, you can get a bit more gain in one direction.

But making a better antenna is harder than just adding some copper, which will destroy the matching / tuning of the antenna and almost certainly make it worse.

Notice that the tree-contacts device on the right hand side is probably a transistor used as a power amplifier for the RF signal, and so its performance is directly coupled to the antenna having the right, probably reactive, impedance. So, actually making this a transmitter with more gain will be more or less a redesign of the RF stage. No way that pays.

Atop of that, changes are it's illegal to increase the gain, as PAPR is limited for ISM devices in most countries.

A better bet would be to replace the antenna of the receiver, which probably is less directly coupled into an amplifier other than being connected via a matched-impedance line, and seeing this does not seem to be a two-way communication link, is not going to break any laws. Or, just replace the whole receiver with an SDR + raspberry pi + relay card, or something.
Form a quad antenna by adding passive reflector and/or director elements on the outside of the case. The physical dimensions of the case/PCB would need to be capable of providing appropriate separation between passive and driven elements.