Someone was making havdallah and another person was there who decided to not have kavana (intention) to fufill their obligation of the aish (fire) part of havdallah with that person. In the middle of the bracha (for example after they said "Baruch Atah HaShem Elokeinu Melech Ha'Olam...") the person decided they yes wanted to be "yotzee" with that bracha. Does there kavana help now in the middle of the bracha (since in reality they did hear the whole bracha) or in order for the kavana to work must they have kavana from the beginning of the bracha? Would there be difference of lichatchila and b'dieved?
This is discussed in Shulchan Aruch 213:3 it seems one has to,hear every word and the motzei has to have the yotzei in mind.The Mishna Brurah seems to say the same,but the Shar Hatziyon 20 brings that missing some word one can still yotzei bdeieved,but not miss the ikar of the bracha ,like Baruch atah... It is best to see the halachas inside and see how your case fits because the halacha is there just applying it to your case is not so simple because of maybe Stam daas to be yotzei .what was the persons intention?