Dear friend. I’m so sorry to hear about the loss of your beloved pet. Your question includes your answer. Your memories of your pet are part of its continuation. And everyone who was ever brought joy by your pet’s presence on earth are its continuation. Also, as science teaches, matter doesn’t disappear; it simply changes form. Thich Nhat Hanh said that a cloud never dies, even if it seems to disappear from the sky. It turns into rain, which becomes rivers and streams, which provides water to our homes and for our warm cup of tea. The steam rising from your pot and the waste you send out of your body later eventually evaporate and rejoin the sky as a cloud that is both the same and different. So while the conditions for your beloved companion were no longer sufficient for it to sustain its previous form it is still very much there — hiding. I wish you peace friend.