Praise be to Allah.
It is obligatory to pay zakaah on shares if the owner intends to sell them and they reached the nisaab (minimum threshold). He should work out their value each year, i.e., find out their market value, and pay one quarter of one tenth (2.5%) of their value.
The nisaab is the equivalent of 595 grams of silver or 85 grams of gold. As silver is of lesser value, the nisaab should be worked out on the basis of silver, so as to give the poor their fair share.
So if a person owns shares the value of which is equal to the value of 595 grams of silver, then he owns the minimum amount.
If a person acquires shares with the intention of benefiting from their dividends and profits, and he does not intend to sell them, then he does not have to pay zakaah on the share itself; rather he has to pay zakaah on the dividends, if he has taken possession of them and one zakaah year has passed; he should pay one quarter of one tenth, or 2.5%, (of the dividend).
If the person does not have complete ownership of the shares, or he is not allowed to dispose of them, like the shares which the company has given to your husband, then he should pay zakaah once when selling them or taking back their value, or when obtaining full possession of them by completing five years of work in that company.
Zakaah is obligatory upon the owner; if you have shares then you must pay zakaah on them, and you are responsible for that, but the husband may voluntarily pay zakaah on behalf of his wife.
The basic principle is that taxes cannot take the place of zakaah; every time one full hijri year passes, you should work out the value of the shares and pay zakaah of one quarter of one tenth.
With regard to the double shares, if your husband will take possession of them after five years and we said that your husband should pay zakaah for one year when selling them, then he should pay zakaah on what remains of their price after paying taxes and National Insurance, because in fact he does not possess anything other than that.
If a person owns shares and works out their value at the end of the year, but he does not have cash with which to pay, it is permissible for him to delay zakaah until he acquires cash or sells the shares, but he has to keep a record of that and write down what he owes of zakaah for the first year, the second year and so on. But it is better to hasten to pay zakaah and to be quick in doing good, and to make it easy for oneself, because if the amount of zakaah accumulates, he may feel reluctant to pay it.
We ask Allah to bless you and to protect you from all harm.
And Allah knows best.