に代（か）わって is an expression that will only appear with nouns, conveying that (B) is doing something ‘in place of (A)’, or ‘on behalf of (A)’. This is a combination of the 格助詞（かくじょし） (case marking particle)
に, the う - Verb 代（か）わる ‘to substitute’, and the 接続助詞（せつぞくじょし） (conjunction particle) て.
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妹（いもうと）に代（か）わって、私（わたし）が買（か）い物（もに）に行（い）くことに決（き）まった。
It has been decided that I am going to go shopping in place of my sister.
私（わたし）が彼女（かのじょ）に代（か）わって会議（かいぎ）に出（で）ます。
I will be attending the meeting in place of her.
に代わり may also be used, as this is the formal conjunctive. Also known as the 連用形（れんようけい）.
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タナカさんに代（か）わり、今日（きょう）は私（わたし）があなたたちの担当（たんとう）をします。
In place of Tanaka-san, today, I am going to be in charge of you guys.
世界中（せかいじゅう）ではファックスに代（か）わりメールが主流（しゅりゅう）になったが、日本（にほん）ではまだファックスしか使（つか）わないところが多（おお）い。
All around the world, fax has been replaced by email as the main form of communication, but there still are places in Japan that only use fax.
In this construction,
に is acting as a location marker, rather than specifically meaning ‘for (A)’. What this means is that に代（か）わる is the act of removing (A) from its place, and exchanging it for (B). This is why に代（か）わって may also be used in the meaning of ‘to succeed’, or ‘to replace’, as switching (A) to (B) may be permanent.
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今日（きょう）は社長（しゃちょう）に代（か）わって、私（わたし）が会議（かいぎ）を進（すす）めます。
Today, I will take charge of the meeting in place of the CEO.
父（ちち）に代（か）わって、皆（みんな）に挨拶（あいさつ）をした。
In place of my father, I greeted everyone.