I believe the form of the sentence "If he sends my package to me, that will really make me happy." is the more correct of the two. Although as a native speaker, it sounds better to me as "If he sends my package to me, I will be really happy."
First off, conditional sentences are also known as conditional clauses or 'if' clauses. They express that the action portrayed in the main clause cannot take place if a certain condition expressed in the 'if' clause isn't fulfilled. The conditional sentence we're dealing with is a type I which means that it refers to something happening in the future that is likely to occur. The package being sent is a rather reasonable condition. This sentence therefore combines a simple-present 'if' clause with will+infinitive in the main clause, giving us the sentence "If he sends my package to me, I will be really happy."
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