ANSWER:

Yes, in sha Allaah,  the reward is the same. 

Before starting menses I was reciting Quran on my mushaf, however when I started menses I carried on reciting from where I left off but on my smartphone. Intention is to complete the whole Quran in Arabic. Would this method of reciting some on my mushaf and some on my smartphone have the same reward as completing the whole mushaf?