Substitution old_email and new_email ?

yes we have already implemented in my custom plugin the method

and this work well..

You should fire the above after every profile update so it always remains up to date. You should handle whether you need to do an actual update or not in your 3rd party solutions endpoint. So for example if I called the above then whenever the HTTP request is processed it should check if any of those have changed comparing against existing values and if they have then save and if not then just disregard the request.

I don't understand well here... As I said, I need to sync data between each server. So if user update his profile, is necessary to always fire the request. So when you say "it should check if any of those have changed comparing against existing values and if they have then save and if not then just disregard the request" you mean about which value I must compare ? The one present in CB or the one present in remote server ?

My goal was to first check if the remote server is well available and reachable (because maybe he can be down for maintenance or any other reason). So if I update data in CB and the request do not reach the remote server, data will not be sync...reason why I thinking to use BeforeUserUpdate.

any clue?

Just fire your HTTP request on every profile update to constantly keep your external system up to date. Disregard checking if something changed or not, just always send the HTTP request after profile update. If the HTTP request fails due to not being able to reach your external system then next update will try again. All of this is done silently so this gives it the best chance of keeping your external system up to date.

then next update will try again.

What do you mean by this ? If user update his profile for example the next time he login (could be days after) ? Or you mean to build something who will attempt again and again to reach remote server until data is updated?

In both case this is not ideal for me because data between each server must absolutely be always equal each seconds/minutes. If for example a user update without problem his email in Joomla/CB but the new email was not transmitted on remote server, user will never be able to be connected to remote server. I cannot take the risk to have a user who have different email in both system. This is the reason why I prefer before be sure to be able to reach remote server. If is not possible, CB profile must not be updated and in this case data are always equal even if not updated.

What do you mean by this ? If user update his profile for example the next time he login (could be days after) ? Or you mean to build something who will attempt again and again to reach remote server until data is updated?

If the first request failed for whatever reason then the next time he updates his profile it'll try again. I suppose you could also execute your request on login too if you wanted.

In both case this is not ideal for me because data between each server must absolutely be always equal each seconds/minutes. If for example a user update without problem his email in Joomla/CB but the new email was not transmitted on remote server, user will never be able to be connected to remote server. I cannot take the risk to have a user who have different email in both system. This is the reason why I prefer before be sure to be able to reach remote server. If is not possible, CB profile must not be updated and in this case data are always equal even if not updated.

It will be assuming the connection to your external server does not fail. Fire your action after registration, after login, and after profile update and you shouldn't have any problems keeping them synchronized. There's no way for you to keep them synchronized down to the very second firing it on those 3 triggers every time is your best option to keep it synchronized.