Short Answer: There's no special official word for this in English, one that would succinctly specify it on a government form.
Longer Answer: In questions like 'Is there a word for [some description] in [some language], there are a number of issues. There is the social issue of whether the culture recognizes the concept as natural, if the concept occurs often enough, whether it is taboo or important or hardly of concern. There is officialese or neologism, people making words up to fit the situation, or legalese, terms created to fill a slot created by legislative fiat distinguishing one concept from another because, say, generations ago someone sued someone else for money from an estate. Then there is the labeling problem, what you call something, how you refer to it (by noun, verb or adjective), how you refer to the name, what the thing is (those all sound the same but could be very different).
In this situation, yes, English can describe the situation (as you have done). In English, a person who has married 'is married', and if their spouse dies they 'are a widow(er)', and if they then remarry, they're just back to being 'married'. It is their 'second marriage', the spouse 'is the second husband/wife', the children of the second spouse (from a previous marriage) 'are step-children' and the relation between the children of the previous spouse and the new spouse 'are half-brothers/half-sisters'.
If forced to say something in that slot, 'second wife/husband' I think would be sufficient translation. The corresponding form in any other country may or may not mention the deceased prior spouse. It could be important for taxes or estate assessment or a census, all depending on the administrative results desired.
Away from the form, that person is 'called his wife' and 'is the second wife'. (in some cultures, one calls some relatives by number, eg sons by birth order in Chinese).
But for the situation on the form, in English, there is no special single word for it (and no set phrase for it either, it's just a spouse, which just happens not to be the first one).