Just add a little phrase at the beginning: "If it is possible, may that dog be able to so and so..." saying exactly the same phrase. Add "If it is possible...". as well, for people that have died. Add a phrase at the beginning: "If rebirth is true, may so and so...", and do exactly the same phrase. Just by adding that little phrase in the beginning that's enough and then the rest of the wish can be exactly the same.