see this link https://imgur.com/a/o0HViw9  of image  

 it is normal to continue between these two clues as you can see the image I put in ?

good, seen from behind the antenna. still has left pin to middle pin connection when it shouldn't have
I already cut the line between the first track and the second, and is giving me continuity with the multimeter when it should no longer. it's normal ??

Basically you gently expose the small bits of copper (image 4 is the best) with a knife as per the images in the post. Then you solder between the 2 contact points.. i.e you bridge a contact between the 2 points.

I've managed to find a more detailed guide at the link below. It's in Italian but a simple google translate does the job.

https://hassiohelp.eu/2019/03/02/zigbee-cc2531-antenna/

before and after as reported by zigbee2mqtt link quality on a router. Red arrow was where the antenna was installed. https://www.screencast.com/t/3C9ZDwjTW

Put a phone light/torch behind the old antenna and I believe you will see that there's a bridge to ground in a lower layer of the PCB - triangular shape object. This looks to go to the visible trace closest to the corner where the new connector fits.

That might explain the results @MikeCC and @data found?

It would be interesting to test without the edge ground pin on the SMA connector soldered to the trace as then I don't think the connection will be made.

Just look at the schematics at https://www.mikrocontroller.net/attachment/366900/Antenne.jpg and you will see, that the rf coupler (named B1) is grounded.  When you cut the antenna trace to the right there is still the ground connection via B1...

Hello @data , sorry I'm very beginner at this and I've never done any type of mod before, I want to make sure I am doing this correctly. Do I cut the places I circled in red and solder the place I circle in blue? Thank you.  https://i.imgur.com/8vavkRZ.png

@data does it make a big difference?

(parts are ordered, will make this also! THANKS)

Both are fine, but optional. If you are not sure, just omit it...

I have cut / removed the pcb at the two points as visible on the photo. Then I checked if there is still a connection between ground and the point where I have to connect the antenna. Surprisingly there is still a connection between ground an antenna connector although I cut the pcb at the two points. This is not correct, right? Is there any other point I have to cut/remove?

I just checked with one of my adapters with a multimeter, and there is indeed still a connection to ground. Since I don't have the schematics at hand at the moment,  I can't tell why it is there. Maybe it is due to some rf-frontend protection circuit which shorts unwanted voltages to ground.
However, the antenna works, at least according to the improved signal I get. 

With my multimeter I measure 0 Ohm resistance between antenna connector and ground. So this means that it doesn't make any sense to cut the two points from pcb, right?

You can find schematics here:

http://www.ti.com/lit/ds/symlink/cc2531.pdf

https://www.mikrocontroller.net/attachment/366900/Antenne.jpg

I just checked the schematics: the measured connection between the antenna output and ground is fine, since it is connected via R9 (0 Ohm) and B1 (rf-coupler) to ground.

What do you mean with 'it doesn't make any sense to cut the two points'?

Since you've asked this question, I guess you have no idea of high-frequency/RF signals. The RF-Frontend of your stick consists of R9, C5 and B1. Simply said, this frontend is designed and built in such a way, that DC voltage and all unwanted signals (other frequencies than 2.4GHz) are shorted to ground so that only the 2.4GHz frequency signal is fed into the chipset.

Hence it makes complete sense if you measure a ground connection with your multimeter. And of course you still need to remove the stripline the way explained. The distance between signal and ground is vital in order to maintain impedance. See e.g. https://en.wikipedia.org/wiki/Impedance_matching

How you do it shouldn't make much difference. But it is probably easier to just bridge the small gap with some solder.

Actually, the best would be to keep the ground connection as short as possible and make  a short bridge to the resistor next to the ground-leg. However, the risk that you accidentally remove/displace the resistor is too big.

". Then you can solder the adapter to the board. To improve the ground connection of your socket, it is reasonable to also connect the now defunct rest of the antenna trace to ground. This gives proper grounding to your socket from both sides. "

The ground connection is improving the signal? Do you mean connecting like this? 

https://imgur.com/a/qSaHPb8

Or do you mean soldering like this?

https://imgur.com/a/hZcj3zN

Which one is it? I want to do this antenna-mod myself. To me your first pic makes the most sense. No RF-antenna-part running as ground. I could be wrong though...