戸籍上の縁は切れても、昔日の絆はそのままだ。

tbd

Our connection may be cut on paper but the bonds of old remain as they were.

これはおそらく戸籍上の出生年月日を調べた上で修正したのではないかと思います。

tbd

I believe this may be a correction after investigation of his date of birth in the family register.

彼女はまだ夫の戸籍に入っていない。

tbd

She has not yet had her name entered in her husband's family.