It would'n work this way. Are you connected to Firefox Account on both devices? After pressing Share all tabs you have to select the desktop Firefox under 'SEND TO DEVICE.

No, I want to save my links to file, not send it to to desktop, that can be off, also I don't want open all of them, just bookmark Again, Firefox allows copy links to clipboard for saving in txt then I there a way to store links as HTML or PDF with links captions, appropriate for importing to desktop Firefox?

I had this same problem. As you pointed out, Aslan7470, the article is not clear. You want to transfer from one phone to the other, but you will need your DESKTOP to do it. Sign in on your desktop and then get the desktop to connect Firefox on another device. It will display a QR code. Scan this from within Firefox, not your camera. On the phone that is the source, you will sync to the desktop. Then from the destination phone you will select sync and use your desktop to connect to the new device.

From the source phone, you can now sync to the destination phone. On the destination device, your tabs can be found by tapping the square with the number of open tabs. There's an icon that looks kinda like a phone on top of a monitor. That shows all the tabs on the source device. You will have to click on each tab to import it to your destination phone.

In summary, you need to register your devices with the desktop to transfer between devices.

The desktop acts as a sort of bridge to connect devices. I was able to copy my open tabs and it even transferred my passwords for the websites.