A claim of responsibility for an arson attack on a car, posted anonymously on an animal rights website, is being investigated by Sussex Police.
Mrs Grant's late husband was director of a pharmaceuticals firm
Police said Kathryn Grant's BMW was set on fire at her Hove home in October.
Her husband, who died last year, was director of a drugs firm said to have links with Huntingdon Life Sciences, Cambs, which uses animals for research.
The web message said protesters planted two incendiary devices under the four-wheel drive, destroying it.
The website message suggests that arsonists knew Alexander Grant was dead when they struck on 13 October, badly damaging the car.
Police said the vehicle was parked close to the house and the incident could have been "far more serious than it was".
The message claims: "We were planning an attack on Grant a few months ago, but then realised that he had just died of a heart attack.
"In October we carried out the operation at Grant's address planting two incendiary devices under an expensive four-wheel drive totally destroying it.
"People who sign contracts with or deal with Huntingdon need to realise that your decisions will come back to haunt you forever, even when you have gone."
A spokeswoman for Sussex Police said officers were investigating whether animal extremists were behind the attack.
She said: "It is one line of inquiry that we will be following up."
She also said she did not know how easy it would be to trace who posted the message on the internet.