Idol theory is the term used to explain how a piece of the whole or an imitation of the real thing can retain a certain amount of the sources power. This is the basis of how imitative magic works and is wielded by magicians. This encompasses most magic used in To Aru. With the use of imitative magic two similar things influence each other as Idol Theory postulates that duplicates retain the properties, attributes, and powers of the original source.

“Idol Theory is a form of basic knowledge that allows us to put the power of God and angels to good use. According to this theory, if one were to build a duplicate of the cross on which Christ was crucified and put it on the roof of a church, some of the holy power from those actual cross-wielders will be replicated. The power of the duplicate is not even 0.000000000001% of the original’s— even the greatest legendary duplicate, Holy Manger, contains only a small fraction of that power—but if someone obtained even 1% of the original’s power, they could match even the Twelve Apostles.”
(To Aru Majutsu no Index Volume 7, pg 64)

Likewise, Fiamma of the Right holds the embodiment of the power of the right hand within Christianity. In addition to being born with the innate attribute and alignment to Archangel Michael who occupies God's Right Seat in heaven, his power is derived from the symbolic prominence the right hand has in christian lore. Therefore The Holy Right is capable of replicating the power all of these original acts held.