Simply replace the unfilled areas such as "[]" and "[date]" with your information.
Dear [name],
I was so sorry to hear about the loss of [pet's name]. [He/She] was such a [adjective] and [adjective] [type of animal]. [He/She] was so devoted to you and I know that you loved [him/her] very much.
Sometimes, losing a pet can be as hard as losing a friend or family member. In some ways, it might be harder. There are never any negative memories or emotions associated with a pet, only joy. A [type of animal] can never hurt your feelings and there are rarely any regrets.
I know you will miss [Pet Name], [he/she] was a good [boy/girl]. I wish that you weren't hurting. If there is anything I can do for you, don't hesitate to ask.
Sincerely,