Hello, and thanks for your post,

I am sorry to hear about your father.

Because the chickenpox vaccine is live, there is a very small risk that someone who has been vaccinated could pass on the virus to someone who is not immune to chickenpox. This is usually only a risk if the person who has been vaccinated develops a chickenpox type rash at the injection site or elsewhere on the body. You can read more about this here

So, if your father has had chickenpox, he will already have immunity, so the risk is even smaller. Most live vaccines take around 14 days to develop immunity. So if your son didn't have a rash after his vaccination, then transmission is unlikely. 

There is other general information on the NHS website, here and here

I hope that this helps you make a decision. You can also ring your GP or NHS 111 for further medical advice as well. 

All the best,

Catherine