If the criminal courts did not make a compensation order, you are going to have to obtain a civil judgment against the thief and then enforce it by one of the many ways available through the civil courts. It should be simplicity itself to obtain the civil judgment as there is undeniable proof of liability in the conviction. The main question here however is whether this person that stole your horse is in a financial position to pay any judgment.
The other question which springs to mind is what has happened to the animal. You would certainly be able to recover it from anyone to whom it had been sold.
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• Get a divorce
• Have contact with my children
• Make a small claim
•Write a letter of claim
•Obtain a Grant of Probate
•Get legal advice and help with my case
•Make a Will
•Change my Name
•Prepare a legally binding agreement
• Sever a Joint tenancy
• Prepare a Partnership Agreement
• Sell a Jointly owned Property
• Appoint a Guardian for my children