Words for a real moment
What to say to someone who lost a pet
A pet can be family. Acknowledge the loss directly and leave room for memories without asking them to minimise it.

Words you can use
A ready-to-send version
I know how much your pet meant to you, and I’m thinking of you. I can listen for ten minutes or simply send a quiet hello. Say yes, no, or nothing at all — I will follow your lead. If today is not right, that is completely fine.
A useful approach
Acknowledge the pet’s death directly and do not compare it with another loss.
Give them a choice between a brief chat and a message they can answer later.
Leave the offer open for today; do not send another message until tomorrow.
Make it fit your person
Change the relationship, timing and tone
No name is needed. Optional details are not stored.