These wise words from the late John Hayward, who used to run The National Theft Register are worth repeating:

To help stem the ever-increasing thefts of parrots I would appeal to all Bird Keepers to ensure that their Birds can be POSITIVELY IDENTIFIED either by close ring or microchip, or both.

The best deterrent is to catch the thieves and have them convicted and birds recovered.
The Police have limited resources and will not investigate thefts of stolen property of any kind if it cannot be properly identified.
If you can't prove the bird stolen you can't expect to prove a case of theft against anyone.
Your several thousand pound motor car is identifiable so why not your valuable birds!
The thieves will invariably visit prior to the theft to research alarm systems and the ' lie of the land'.
It is essential therefore for everyone with BirdHouses, Aviaries, Collections and Shops to be particularly vigilant and to note any suspicious incident and especially to record details of any suspect motor vehicle.
Any such incidents should be reported immediately to the Office, as whenever any theft occurs and in reported, the more information we can give to the Police, the better will be the response.
There is little doubt that the CITES Controls are having some effect.
Due to the restrictions of import/export from the Wild, at times demand is greater than the supply and therefore our captive birds come under attack.
The message therefore is 'Don't make it easy for the thief. Ring and Microchip your birds. Retain feathers and store in a secure signed and dated envelope - (as a 'control sample') and consider having a small sample of blood taken the next time you visit the Vet, again for identification purposes. D.N.A. now exists for comparison and identification purposes.'
Anyone offered an Annex A bird, for example a Scarlet Macaw, African Grey Parrot, Goffin's or Moluccan Cockatoo, Cuban Amazon etc. should demand and examine the necessary documentation.
We drastically need to reduce the numbers of our birds being stolen.
They are intelligent sensitive creatures and the stress of being forced into bags and boxes by thieves wearing balaclavas in the dead of night is the most cruel of criminal activity.
Very often, they do not survive the trauma, we lose the future breeding programmes but ultimately it is the very welfare of these beautiful ENDANGERED SPECIES that is the primary concern.
Finally, I recommend that bird-keepers consider Insurance cover by one of the Specialist Companies, especially for theft and Vets' fees and that you join the Parrot Society UK or other dedicated Clubs depending on the species.

See also - Parrot Insurance