We proposed the method for non-destructively embedding information inside a 3D fabricated object very clearly by the process of re-magnetization. Our strong points are that the 3D object is finished (ready to use) after only a printing process, and is able to be reused by re-writing information many times. In this paper, we investigated the effects of the depth (positions inside the object) of the storage cell, which is printed as a ferromagnetic filament, on the clarity of the embedded information. Our purpose: we need to find the conditions that gave the most benefit in both obtaining high magnetic strength and protecting the embedded information. With this advantage, the method leads to the production of creating the high-quality household 4D object, the personal interactive 3D object, in the near future.