Fullerenes have unique chemistry owing to their cage structure, their richness in pi-electrons, and their large polarizabilities. They can trap atoms and small molecules to generate endohedral complexes as superconductors, drug carriers, molecular reactors, and ferroelectric materials. An important goal is to develop effective methods that can affect the behavior of the atoms and small molecules trapped inside the cage. In this paper, the quantum chemical density functional theory was employed to demonstrate that the stability and position of a guest molecule inside the C60 cage can be changed, and its orientation controlled, by modifying the C60 cage shell. The outside attachment of two hydrogen atoms to two adjacent carbon atoms located between two six-membered rings of the C60 cage affects the orientation of the LiF molecule inside and increases the stability of LiF inside the cage by 45%. In contrast, when 60 hydrogen atoms were attached to the outside surface of the C60 cage, thus transforming all C=C double bonds into single bonds, the stability of the LiF inside was reduced by 34%. If two adjacent carbon atoms were removed from C60, the stability of LiF inside this defect C60 was reduced by 41%.