"Invalid web site provided" after moving WP to a directory

Correction: I mean that my site is now https://localhost/en , not https://localhost/en)

Interesting is that Sucuri works fine my live site, baruchyoussin.com, which is supposed to be practically identical to the localhost site.
Both sites have 3 WP installs, baruchyoussin.com/en , baruchyoussin.com/ru , baruchyoussin.com/he (localhost/en , localhost/ru , localhost/he ), and on all three installs behavior is the same: Sucuri works fine on baruchyoussin.com and reports Invalid site on localhost.
Thanks for your help.

This is not an issue actually, the “Malware Scan” page is simply a wrapper around a service named “SiteCheck” [1] which a web application that acts as a remote scanner, this means that to get the information it contacts a website to read its content and report suspicious code.

You are trying to make SiteCheck scan a website that is not accessible from outside your local network, localhost is not accessible from outside your LAN so the malware scan tool can not report anything at all. It works in your live site because it is accessible via a public network node.

I recommend you to read this article [2] that explains how “Localhost” works and what it means to be non-accessible from outside your local network [3].

[1] https://sitecheck.sucuri.net/
[2] https://en.wikipedia.org/wiki/Localhost
[3] https://en.wikipedia.org/wiki/Local_area_network

Yorman,
Thank you very much for your clarification. I understand my mistake about sitecheck and localhost.
As for my complaint about Core Integrity, I checked that it works on both localhost and the live site.
Thanks for your help and your great service!