I saw a suggestion to use a smash tool. Not wanting to hijack that thread I ask here: What is smash tool for?
Take a look here:
It makes it possible to move the silkscreen-annotation of a part. Basically it unties the silkscreen annotation from the part, such that you can move the annotation to where you want it to be.
For those who wonder where the name comes from. It’s named that way in EAGLE and I couldn’t think of a more descriptive name.