In Siman שיח the mishne breruah, in Sif Koton לא after bringing פשט from the פרי מגדים, says that because it was nishreh in a Kli Rishon on erev shabbos then now (on shabbos) you can be shoireh it in a kli sheine. If a kli sheine is not mevashel then why only because it was in a kli rishon on erev shabbos is it allowed?
Even though כלי שני אינו מבשל nevertheless, we are still not allowed to put foods into a kli sheini for one of two reasons. See Mishna Berura 318-34 because when food is put into a kli sheini it looks like cooking (however precooked food doesn’t appear as if it is being cooked now). Secondly, (see M:B 318-42) that a kli sheini can cook קלי הבישול, such as salty fish, tea leaves, etc. We also don’t know what is considered קלי הבישול and what isn’t, therefore in general we don’t place non cooked foods in a kli sheini. Says the Pri Megadim, that if the food was soaked in a kli rishon, we don’t have a fear that it will get cooked in a kli shieini, and therefore it may be placed inside it.