Half moustache is present only on one side or patches of hair loss,  or density of moustache is less?  It needs to be seen in person.  If any pathology is there it can be corrected medically.  However,  if it has been the normal tendency ever since you started growing a moustache,  then that can't be altered much.  I do hair transplant for beard and moustache areas to increase hair count to cover up.  That will be the final option.