Your brother does not have to pay tax on the money when it is moved. You won't have to pay federal or New Hampshire tax on the money since an inheritance is not taxable. If your brother was named as the sole heir to the money, then the payment to you would involve gift taxes, otherwise if you inherited your share, then there would be no gift tax issues as the money would not be a gift.
A gift is taxable to the giver, so your brother would be the only one potentially subject to a gift tax. There is a federal lifetime exemption of 13.61 million dollars for gifts in 2024, so it is not likely there would be any gift tax involved.
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