From your comments,
it seems your partner's family register [koseki] has been managed by Kyoto City.
He needs to know
in what Ward of Kyoto City his registered domicile [honseki] is settled.
(If he is not sure and he still has that koseki tohon handed before marriage,
he checks the description of his honseki.)
When he submits his marriage notification [kon'in todoke] at the office of that Ward,
his family register certificate is not necessary.
He can send by postal mail to that Ward Office
his request for his family register certificate to be sent to his registered Tokyo address. https://www.city.kyoto.lg.jp/bunshi/page/0000145608.html
The handling fee 450 yen is to be paid with Teigaku Kogawase Shousho,
which is issued by Japan Post Bank and available at a post office.
The issuance fee is 100 yen. https://www.jp-bank.japanpost.jp/kojin/sokin/hikoza/kj_sk_hkz_kogawase...
Koseki touhon is a (complete) transcript [touhon] of a family register [koseki].
Kyoto City recently computerized its family register management;
now a certificate of all the matters / individual matters
works the same as a former transcript / abstract.
For his purpose of marriage notification [kon'in todoke],
a certificate of individual matters [kojin jikou shoumeisho] is enough. We both live in Tokyo but not at the same house, because I live in my companyfs rent house.
Are you and he registered as residents to the same City?