(however late he is -),mother will wait for him to have dinn

however 用作连接副词,相当于no matter how,引导让步状语从句,意思是“不管怎样……”“无论如何……”,具体结构有以下两种：
1．however+形容词+主语+系动词,例：
However rich people are,they always seem anxious to take more money.
无论人们有多富裕,他们似乎总是渴望挣到更多的钱.
2．however+副词+主语+谓语,例：
However fast he runs,he can’t catch up with us.无论他跑得多快也不能赶上我们.
你这句话属于第一种