EAGLE - set part to a different layer without mirroring it
OK, I think I understand based on your comment. You want the silkscreen to move to the bottom for one of the two headers you've depicted. The easiest way to achieve that will be to make a duplicate library part, then reassign the layer of the silkcreen from tPlace to bPlace. Then in your schematic, replace the component(s) you want to be drawn on the back with your duplicate library component by right-clicking on it and choosing &quot;Replace&quot; and selecting it from library.
Changing the layer of the silkscreen in the library editor is most easily achieved by turning off all the layers except tPlace, then use the &quot;Wrench&quot; tool to select Layer =&gt; bPlace and just click on all the tPlace segments. You can speed this up a little by using the select area tool first to select the whole group at once, then click the Wrench tool, then click to apply to the whole group at once.