Both man and animal are trichotomous, having both a soul and a spirit: “Now may the God of peace Himself sanctify you entirely; and may your spirit and soul and body be preserved complete, without blame at the coming of our Lord Jesus Christ.” (1 Thessalonians 5:23)

Animals are described as “living creatures/souls” in genesis with exactly the same word as the soul in man [soul/nephesh].

Animals are called living creatures in Genesis and there are living creatures in heaven in Revelation:

Living creatures in Genesis:

“Now behold, I Myself do establish My covenant with you, and with your descendants after you; and with every living creature  [soul/nephesh] that is with you, the birds, the cattle, and every beast of the earth with you; of all that comes out of the ark, even every beast of the earth.” (Genesis 9:9–10)

Revelation has living creatures in heaven:

“Out from the throne come flashes of lightning and sounds and peals of thunder. And there were seven lamps of fire burning before the throne, which are the seven Spirits of God; and before the throne there was something like a sea of glass, like crystal; and in the center and around the throne, four living creatures full of eyes in front and behind. The first creature was like a lion, and the second creature like a calf, and the third creature had a face like that of a man, and the fourth creature was like a flying eagle. And the four living creatures, each one of them having six wings, are full of eyes around and within; and day and night they do not cease to say, “Holy, holy, holy is the Lord God, the Almighty, who was and who is and who is to come.” And when the living creatures give glory and honor and thanks to Him who sits on the throne, to Him who lives forever and ever,” (Revelation 4:5–9)

 “And the wolf will dwell with the lamb, And the leopard will lie down with the young goat, And the calf and the young lion and the fatling together; And a little boy will lead them. Also the cow and the bear will graze, Their young will lie down together, And the lion will eat straw like the ox. The nursing child will play by the hole of the cobra, And the weaned child will put his hand on the viper’s den.” (Isaiah 11:6–8)

“The wolf and the lamb will graze together, and the lion will eat straw like the ox; and dust will be the serpent’s food. They will do no evil or harm in all My holy mountain,” says the LORD.” (Isaiah 65:25)

“In that day there will be inscribed on the bells of the horses, “HOLY TO THE LORD.” And the cooking pots in the LORD’S house will be like the bowls before the altar.” (Zechariah 14:20)

Ontologically, man and animal are not much different:

Animals have the SAME feelings of anger, love, fear, affection, aggression, stubbornness, independence, freewill etc. Animals have recognizable personality just like man.

Memory in man does not reside in the physical brain but the spirit. The rich man and Lazarus were dead and their brains were dust, yet notice all the things they remembered and knew in addition to retaining their personalities and identity.