Thanks for your help, you both!
I just had some time again and so I've worked on a little bit on my project.
Unfortunately, I found a bug in the program.
As already said, I plan to redirect the Output of a Minecraft Server into a TMemo.
KpjComp's solution works very well for all programs I've just tested (thanks for that again

!) but there's a error with the Minecraft Server. When I start the process, the server, it redirects the first two lines of the output and then the program hangs up/freezes.
That's a pitty, because your solution works for all other programs

!
Thanks in advance (again

) and many greetings,
Lazarus