If he would die within seven years of his divorce, can his ex-wife come and take his money from our savings?

There is no automatic right of a former spouse to receive any money from the estate of a deceased ex-husband or ex-wife. Unless the divorce decree has a specific provision concerning inheritance, the ex-wife would receive nothing - which is generally the case. Usually, if the decree has a death payment to the former spouse, it's in the form of a life insurance policy.