Praise be to Allah.
If you started the company with your own money, then you have the right to retain ownership of the company completely in your name from now, and not after your husband dies, but you should work out your husband’s share of this company in return for the work he did and his running of the company, either in the form of a sum of money that he takes in return for that, or in the form of a portion of the shares equivalent to the work he did.
In that case, you will have protected your rights and your property and your husband will have his rights commensurate with his work.
Then if your husband dies, the wealth that he leaves behind will be shared out, whether it came from this company or otherwise, among all of his heirs, including the children he had before he married you, and his second wife, according to the shares allocated to them in sharee‘ah.
If the official papers are in your husband’s name, he can correct that and put them in order from now; that should not be left until after he dies.
If he cannot do anything about that now, or if it will adversely affect your company, then he can write that in the form of a will.
But he should not bequeath anything of his private wealth to you, because he does not have the right to make a bequest to any of his heirs from his wealth. Allah has allocated to them what they are entitled to as inheritance. Rather he is only documenting your original right to the company. The Prophet (blessings and peace of Allah be upon him) said: “Allah has given everyone who has rights his rights, and there is no bequest to an heir.” Narrated by Abu Dawood, 2870; classed as saheeh by al-Albaani (may Allah have mercy on him) in Irwa’ al-Ghaleel, no. 1655. It was also narrated by ad-Daaraqutni (4150) as follows: “It is not permissible to make a bequest to an heir unless (all) the heirs consent to that.” Classed as hasan by al-Haafiz Ibn Hajar in Buloogh al-Maraam.
Ibn Qudaamah (may Allah have mercy on him) said: If he makes a bequest to his heir that the other heirs do not agree to, it is not valid, and there is no difference of opinion among the scholars on this point. Ibn al-Mundhir and Ibn ‘Abd al-Barr said: The scholars are unanimously agreed on that, and there are reports to that effect from the Messenger of Allah (blessings and peace of Allah be upon him). Abu Umaamah narrated: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “Allah has given everyone who has rights his rights, and there is no bequest to an heir.” Narrated by Abu Dawood, Ibn Maajah and at-Tirmidhi. But if they give their consent, it is permissible, according to the majority of scholars.
End quote from al-Mughni, 6/58
And Allah knows best.