He was thinking about his family until the very end.
Until his very end, his thoughts were with his family.
ご質問ありがとうございます。
① "He was thinking about his family"＝「彼は彼の家族のことを考えていた」
"until the very end."＝「最後（の最後）まで。」
("until the end"だけでも良いのですが、「死ぬ直前まで」というニュアンスで"very"を入れています）
② "Until his very end"＝「彼の最後まで」
"his thoughts were with his family."＝「彼は家族のことを思っていた。」
ご参考に。
He was thinking about his family until the very last moment of his life.
おっしゃっている内容は、このように表現することも出来ます(*^_^*)
He was thinking about his family until the very last moment of his life.
「彼は人生の最期の最後の瞬間まで家族のことを考えていた」
last momentで「最後の瞬間」ということですが、それにveryを付けることで、「最後」ということがより強調することができます(*^_^*)
以上です。
少しでも参考になれば幸いです(*^_^*)
He thought about his family right up to the moment he died.
He was thinking about his family until his last breath.
この場合、次のような言い方ができますよ。
ーHe thought about his family right up to the moment he died.
「彼は亡くなる瞬間まで家族のことを思っていた」
ーHe was thinking about his family until his last breath.
「彼は息を引き取るまで家族のことを思っていた」
ここの「最後まで」は right up to the moment one died や until one's last breath を使って表現すると良いでしょう。
ご参考まで！
アメリカ合衆国 
日本 
カナダ 
