If the source of the animal soul is this world or if it is from G-d and at the end vanishes, it would mean that this world is separated from H'. If this was the case Hv'S our One G-d would be an object and not the One. Even if you say He is the Subject and the world is object you are giving Him a size (of not being the object)... Hv'S. Moroever you are telling what is what so you are not just separating the Lord from His creation but your own self from both because the thinker must be detached from the two 'arguments' to speak in those ways. This is very well hidden 'avodà zarah. Basically if the animals are without free will they are still made of G-d and being that H' does not die ever, they won't die either. In which way they still exist is uknown but we could say that if they are just without free will the will come back in H's Own Consciousness or that they are a form of malachim that are usually said to have one heart and not two because of the verse in Vayerà or that they will exist as they would have been in 'Eden, eating just vegetables and without attacking one another. Lot of options you can have but not REAL DISPEARREANCE of anything because it would mean the H' has a 'hole somewhere' Hv'S! Rambam could be explained in other ways, he says that an animal is lost and this is used as a metaphore, but this does not mean the the animal'soul after death is no more, but that the animal during this life is lost and lives with difficulties because of the sin of men. It could be read in different ways. I usually say if peloni does so and so will be lost like a dog roaming around but this does not mean that the dog will roam in the afterlife. Maybe mr Peloni Hv'S will roam in the afterlife because he has done 5% of his good potential but the dog in the case we say that he does not have free will at all will have done his 100%. He will be rewarded, or he will appear as pure H' will as a malach or something I can't even imagine. My opinion. Sefer, Sofèr and Sippur are in truth just One and so death does not exist at all as a real thing but just as relative. If death is relative G-d is absolute and omnipresent, but if death is real in that very idea the presence of G-d's Counsiousness would l'a disappear and He would be Hv'S relative. So is the gods of other religions: one, two, three... but still objects and not ABSOLUTE ONENESS. B"H Shabbat Shalom umevoràch lekullam!!