The Internet and its numerous platforms such as Amazon are an easy way to make cosmetic products accessible to a great deal of potential consumers all over the world.
However, it is important to remember that any kind of cosmetic products sale targeting EU consumers is subject to EU cosmetic regulations.
That is to say, cosmetic products sold on the Internet and made available for EU consumers should be compliant with EU requirements as if they were sold in a physical store located in the EU. Meaning that each product sold online to European consumers should be notified on CPNP, have a compliant PIF and a designated RP.
Whether it is an EU established website or a non-EU established website, there is no difference: if the final consumer of the products is based in one of the EU countries, the same rules are applicable.
Also, note that samples distributed in stores or online should also have a CPNP number even if they are not for sale.