Just a quick update if someone stumbles upon this question:
I realized this via a Powershell-Script that extracts the ID of the receiving user and the ID of the User that gave the receiving user the group.
It is not ideal because it reads through ALL logfiles when being executed and relies on the "notification" for the group not to be changed in a future update but I guess it is a solid base and maybe you can work out a more refined version with this script as a base 
Code:
#config
$outfilepath="<NAME AND PATH OF THE RESULTSFILE (CSV-FORMAT)"
$logfilespath="<PATH TO THE TS3-SERVER'S /LOG-FOLDER"
$groupid=<YOUR GROUP ID>
$groupname="<NAME OF YOUR GROUP>"
#remove the old outfile before exporting the new list
Remove-Item $outfilepath
#searchstring that is used to determine which lines correlate to the group being "awarded"
$searchWords = "id:(\d+)\) was added to servergroup '"+$groupname+"'\(id:"+$groupid+"\) by client.+id:(\d+)\)"
Foreach ($sw in $searchWords)
{
Get-Childitem -Path $logfilespath -Recurse -include "*.log" |
Select-String -Pattern "$sw" | % {"$($_.matches.groups[1]),$($_.matches.groups[2])"} |
Out-File -Encoding "UTF8" -FilePath $outfilepath -Append
}
The results look like this:
1234,4321
4711,9941
6521,9223
etc.
The first number is the TS-DBID of the user that received the group and the last number is the TS-DBID of the user that received the group.
Feel free to use this script as you like.
Just make sure to notify me of any changes you made to improve the script so I can update this answer and provide ppl with the latest version of it