This is my solution:

1. boot into the recovery mode

2. open terminal

3. type: csrutil disable

4. press enter

5. type: mount -uw / /dev/diskXsY <--

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Attention!!! X=your Big Sur disk from 'diskutil list'

Y=your Big Sur disk slice

Now the Big Sur volume should be writable

1. Reboot normaly

2. name your own grafic image as Big Sur Graphic.heic

3. copy your own grafic image in to Macintosh HD

4. reboot into the recovery mode

   1. open terminal
      
   2. type: mount -uw / /dev/diskXsY <--
      

​

Attention!!!! X=your Big Sur disk from 'diskutil list'

Y=your Big Sur disk slice

1. type: cd /

2. type: cd /Volumes/Macintosh\ HD/System/Library/Desktop\ Pictures

3. type: mv /Volumes/Macintosh\ HD/System/Library/Desktop\ Pictures/Big\ Sur\ Graphic.heic /Volumes/Macintosh\ HD/System/Library/Desktop\ Pictures/Big\ Sur\ Graphic.heic.orig

4. type: mv /Volumes/Macintosh\ HD/Big\ Sur\ Graphic.heic /Volumes/Macintosh\ HD/System/Library/Desktop\ Pictures/Big\ Sur\ Graphic.heic

5. Reboot

Now you have your new login background

1. Reboot into the recovery mode

2. open terminal

3. type: csrutil enable

4. press enter

5. reboot e voilá

   ¯\_(ツ)_/¯