Type Ia supernovae (SNe) are believed to mark the thermonuclear explosion of a white dwarf (WD), but the explosion mechanism is stil unclear. Recently a new theoretical model was proposed, for a binary WD, where the primary WD explodes via a double detonation (despite being of sub-Chandrasekhar mass) while the secondary WD survives and is ejected away. This has been called a “dynamically-driven double-degenerate double-detonation” or D^6. The discovery of hypervelocity stars with GAIA supports this scenario. As part of our ongoing project of making the connection between the explosion physics and the remnant dynamics, we simulated in 3D the evolution of a D6 SN into the SNR phase, up to thousands of years after the explosion. Assuming a uniform ambient medium, we reveal specific signatures of the progenitor system and explosion mechanism. In particular the companion WD produces a large conical shadow in the ejecta. Our work shows the intrinsic diversity of thermonuclear SNe and their remnants.