This should be the best option

https://www.seblod.com/store/extensions/applications/sitemaps-app-for-seblod

not a less expensive solution ? 

I ask the owner but 108 € for the sitemap,  (and only for 6 months) I guess he would ask me not to do or to make the multi site anotherway ... 

Membership also entitles you to use other apps not just this one. Most of the aps include also commercial plugins that you would otherwise need to buy separately.

yes, I understood.

So : the customer has made his sites by an agency, that has not prevent them of that fact, and they only have this request : a sitemap that can work in multisites, they don't need all your apps.

I will ask them, but not sure they are aware to buy your pro offer,

I asked on this forum because perharps a user have another solution

thanks

You could also build it yourself, probably select dynamic used with menu object would do. But to also get all items within conent types you would need to use free object and replicate search query used when you search for items from certain content type, for that you would also need search join plugin and possibly also search query plugin.