I have done a Video above as I am unable move an image to the PSD in the correct size using the move tool. I am sure that there must be some method.
Based on the video, that's its correct size. The image you are moving is smaller (in dimensions) than the destination image. After dragging you could resize it with CTRL+T then SHIFT drag corners.
Understand the first point, but could not implement this one → SHIFT drag corners.
You press SHIFT to retain image aspect ration while resizing.