Basically, a cleft sentence is used to emphasize something other than the main predicate, by turning it into the main predicate. For example, from 私は今日彼にプレゼントをあげる, you can make cleft sentences that focus on 私(は), 今日, 彼(に) or プレゼント(を), by moving them at the end of the sentence:
- 今日彼にプレゼントをあげるのは私だ。
- 私が彼にプレゼントをあげるのは今日だ。
- 今日私がプレゼントをあげるのは彼だ。
- 今日私が彼にあげるのはプレゼントだ。
However, you cannot easily emphasize あげる with this pattern because it is already at the end of the sentence! Likewise, since 延期された is a main predicate that is already at the end of the sentence, it's hard to emphasize it with this pattern. (It's possible to emphasize 試合が alone; 強く雨が降っていたので延期されたのは試合だ。 "It's the game that was postponed due to the heavy rain.")
Still, you can work around this by using a nominalizer and adding another verb such as する, やる or 起こる:
- 強く雨が降っていたために起こったのは、試合が延期されたということだ。
What happened because of the heavy rain is that the game was postponed.
- 私が今日やることは、彼にプレゼントをあげることだ。
What I will do today is to give him a present.