Transmit headers and footers via API from one site to another

I’m trying to have the same header and footer as my WordPress site on another site (that doesn’t use WordPress) with a different domain and hosting. The manager of the other site wants it via API but I have never done it and I’m not very expert and I would like to understand if it is possible or not, and if so how it can be done. You need to have the same header and footer (including the style) so you don’t have to manually change it every time a link in the menu changes. It is feasible ? I know a bit of php, I made the WordPress site theme myself, but I haven’t dealt with this kind of thing yet