Being Yotzei Havdala from a different area:
If one made Havdala in his home and one’s neighbor heard the Havdala from him while he was his inside his own house [i.e. the neighbor’s house], he fulfills his obligation. The neighbor may even drink wine on the basis of the blessing he heard in Havdala even if he was standing at the time he heard Havdala. Even initially one is allowed to make Havdala in his home for the sake of his neighbors who are listening and fulfilling their obligation from a different area.
Having in mind to be Yotzei: This however that one can be Yotzei Kiddush only applies if the person saying Kiddush has in mind to be Motzi the listening neighbor, and that likewise the listening neighbor has intent to fulfill his obligation.
If the person saying the Havdala is not being Yotzei: The above law applies even if the person saying Havdala does not plan to drink the wine and is not being Yotzei with this Havdala, and is simply doing so for the sake of his neighbors who do not know how to say Havdala [and the neighbor is holding a cup of wine in his hand with which he will drink Malei Lugmav and be Yotzei].
If there are feces or idolatry in-between: Some Poskim rule that one may not be Yotzei Havdala from a different area if there is no feces, or idolatry which is considered like feces regarding this matter, found in-between the two areas. [Other Poskim however argue that feces and idolatry do not intervene.] Practically, [although the main ruling is like the lenient opinion] one is [nevertheless] to suspect for the stringent opinion. [However in a time of need, some Poskim rule one may choose to follow the lenient opinion. Others rule one is always to be stringent. See “The Laws of Prayer” chapter ? Halacha ? for the full details of this subject!]
One can even initially be Yotzei Havdala if he is not in the same room or house as the person saying Kiddush, so long as he can hear the words and both he and the person saying it have in mind to be Yotzei/Motzei, and he plans to eat right after Havdala in the area that he heard it from. If however there are feces or idolatry in-between the two areas then one cannot be Yotzei Havdala.
 Admur 55/22 and 213/1; 273/10 regarding Kiddush
 The reason: Although regarding Birchas Hanehnin we rule that one cannot be Yotzei the blessing unless he is sitting together with the person saying the blessing, nevertheless this only applies by optional blessings over food however by blessings which are an obligation, such as the blessings of Kiddush, there is no such requirement. [Admur 213/1; 167/23 and 273/6 regarding the Mikadeish not being Yotzei]
 Admur 213/1 “Even if the person saying Havdala already drank Malei Lugmav and the listeners thus no longer have to drink wine other than for Mitzvah Min Hamuvchar, nevertheless, they are exempt with his blessing”
The reason: As only by optional blessings over food is there a requirement for the listeners to be sitting together with the person saying the blessing. However by blessings which are an obligation, such as the blessings of Havdala, there is no such requirement. Now, since the listeners join the person saying Havdala to fulfill their obligation of Havdala, they therefore also join to fulfill the blessing of Hagafen over the wine [213/1; Tosafus Brachos 43a]
 Admur 273/10 regarding Kiddush
 Admur 273/10 and 213/1; 273/6 and 167/23 [regarding being Yotzei if Mikadeish will not be Yotzei now]; 190/4; See P”M 273 M”Z 1
 Admur 213/1 “And the neighbor hears over the cup in his hand and drinks”
The reason: The reason for this is because a) Somebody has to drink Malei Lugmav of wine so the listeners can be Yotzei Havdala b) The person who made Havdala cannot drink the wine as he does not have in mind to be Yotzei Havdala, and it is forbidden for him to drink prior to Kiddush. [Admur 273/6]
 The reason: Although in general one is not Yotzei Birchas Hanehnin unless the person saying the blessing is also benefiting, nevertheless one is allowed to say Kiddush for another even if he is not being Yotzei, being that the above rule only applies by optional blessings, while the blessing of Kiddush is an obligation. [Admur 167/23 and 273/6]
 Admur 55/22 regarding Amen and Kaddish and Kedusha; Machatzis Hashekel 273/13 that the same applies regarding Kiddush [and Havdala]; Vetzaruch Iyun from Admur ibid who positioned this opinion between the Halacha of Kedusha/Kaddish and being Yotzei, hence implying they only argue regarding if one may answer, Vetzrauch Iyun.
Other opinions: Some Poskim rule the above law only applies to answering for a Davar Shebekidusha and not towards Amen. [See Poskim in Piskeiy Teshuvos 55/30 footnote 212]
 Opinion in Admur ibid; Michaber 55/20; Bahag in name of Rav Yehudaiy Gaon in name of Rav Acha; Mahariy Abuhav in name of Orchos Chaim in name of Rav Achaiy Gaon
 First opinion in Michaber and Admur ibid;
 Implication of Michaber who only brings as Yeish Omrim, and Admur ibid who does not write Vichein Ikkur and simply writes to suspect for their words; Levushei Serud 55/20; Maaseh Rav 47; M”B 55/62 that it is implied from Michaber and Rama that they mainly hold like the lenient opinion; See Shulchan Hatahor 55/8
Other opinions: Some Poskim rule the main opinion follows the stringent opinion. [Kaf Hachaim 55/95]
 Admur ibid; Levushei Serud ibid; Kaf Hachaim 55/95
Other opinions: Some Poskim rule one is only to be stringent regarding Barchu and other matters which mention Hashem’s name, and not regarding Kaddish and Kedusha. [Makor Chaim 55/20; M”B 55/62 in name of Chayeh Adam; Ashel Avraham Butchach]
 Levushei Serud ibid
 Kaf Hachaim 55/95