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When making tea/instant coffee/hot chocolate etc. on Shabbat, it is supposed to be done in three vessels, so that the boiling water cools off and doesn't cook the powder. The urn is the first, then there's an intermediate cup for pouring, and then it gets poured into your cup (teabag goes in after). (See Shmirat Shabbat C'hilchatah 1:57)
If someone forgot to do the cli shlishi, instead adding the tea to the second cup after the water was put in it, can the tea or whatever still be drunk?
As we learnt here , there are opinions that one does not need a Kli-Shlishi for tea.
As a result, if you skipped that step, you can drink the tea.
Why?
Because once there is any valid opinion that what you did is not Chilul Shabbat, then the resultant product is permitted, even if you personally hold like the opposing view, and even if the Shulchan Aruch decided like the opposing opinion.
Source: Kitzur Yalkut Yosef - הנאה ממעשה שבת - בדברים שיש בהם מחלוקת.
נח: כל דבר השנוי במחלוקת הפוסקים אם מותר לעשותו בשבת או אסור, אף אם ההלכה נפסקה בשלחן ערוך לאסור, בדיעבד שעבר ועשה כן אפילו במזיד, מותר ליהנות מדבר זה בשבת, ואין לאסור משום הנאה ממעשה שבת. [ילקו''י שבת כרך ג עמוד עו].
This article also mentions it, in English.
The Ohr Someyach to Hilchos Shabbos 9:2 writes that cooking in a kli sheni is always Rabbinical, even for things which cook easily.
The Mishna Berura (318:3) cites the Gra"h that according to all opinions, if a Rabbinical prohibition is done unintentionally (as in your case, where you just forgot), then it can be eaten even by the person who did the cooking.
As always, CYLOR.
