The aim of this study is to develop an understanding of how virtual objects can be transitioned between 3D Augmented Reality and 2D standard monitor display spaces. The increased availability of Augmented Reality devices, in combination with the prevalence of conventional desktop setups with mouse and keyboard input, gives rise to future hybrid setups in which users may need to transition virtual objects between display spaces. We developed three virtual object transition techniques: Mouse-based, Hand-based, and a Modality Switch (where users can only use the input methods in their respective display spaces). The three techniques were evaluated in a user study (N = 24) alongside a fourth condition in which participants could freely switch between Handand Mouse-based techniques. Participants were tasked with transitioning virtual bricks from 3D space onto the screen, then using the mouse to make fine adjustments, such as choosing the colour of the brick and placing decorations, to then transition them back into 3D space to build with. The Modality Switch technique was not preferred due to higher mental demand. Participants preferred the mouse-based technique, which allowed them to transition the virtual bricks faster.