The customer has created a page "page1", with two links pointing to two other pages. When copying page1 and the two pages under a parent page, the links, in page1, still pointed to the original two pages and not to the copied two pages.
The links were created an absolute path.
For instance:
/cms/{mode}/{lang}/sites/mySite/home/parent1/p2-parent1.html
/cms/{mode}/{lang}/sites/mySite/home/parent1/p3-parent1.html
The solution was to create relative links as below:
p2-parent1.html
p3-parent1.html