KiCAD is a very nice EDA software, but it try to avoid copying blocks from a schematic to another (from different projects in this case).
Don’t worry! There is a way to you do that:
1) Select the block you want to copy; 2) Using the right mouse button select: "Save Block"; 3) Insert a Hierarchical Sheet: menu Place -> Hierarchical Sheet; 4) Choose a "File name" for new sheet and click OK; 5) Press ESC and double click over the Hierarchical Sheet block; 6) Past (Ctrl+V) the saved block in this new sheet, save and close; 7) Open the other schematic where you want to include this block and import it: File -> Import Schematic Sheet Content
It might be easier, but KiCAD folks want to avoid users to mess.