The final location of Penny (Kaley Cuoco) and Amy's (Mayim Bialik) gigantic painting creates a The Big Bang Theory plot hole. When Amy was introduced at the end of season 3, she was poised to be the female version of Sheldon (Jim Parsons), which is why the pair immediately clicked and after several years of dating got married. Unlike her husband, however, the neurobiologist was less rigid and actually interested in socializing. Early on, she was already unabashedly drawn to Penny and was fascinated by her beauty and charm.
Amy never hid her admiration for the future Mrs. Hofstadter, regularly asking her about her dating escapades and beauty routine. This made Penny uncomfortable at times but as she did with Sheldon, she continued to indulge her new friend. Together with Bernadette (Melissa Rauch), the trio created their own bond and as time went by, they, too, became as close as the boys. Amy, however, continued to be fixated with Penny and did everything to please her and there were several instances that she went overboard, including that time that she commissioned a gigantic portrait of them together.
In The Big Bang Theory season 5, episode 17 titled "The Rothman Disintegration," Amy gifted Penny a painting of them together which she commissioned for $3,000. The illustration features her grinning, while Penny smiled awkwardly. Not wanting to hurt Amy's feelings, Penny accepted the artwork and had it hanging in her apartment on the same wall as the entertainment center. It stayed there until season 10, episode 10 titled "The Property Division Collision" when Sheldon and Amy moved in together in Apartment 4B, while the newly-married Leonard and Penny take the bigger unit across the hall. As Amy settles in her new accommodations, she noticed that the painting was left in Penny's old apartment and assumed that her best friend would want it in her new home. This prompted her and Sheldon to carry it to Apartment 4A to give it to Penny who was understandably reluctant to accept it. Unfortunately for her, she couldn't bear risking Amy's feelings, so in the end, she just took it. At the end of the episode, the Hofstadters were seen mounting the portrait on their wall.
The problem is that the painting somehow made its way back to Apartment 4B not long after. In The Big Bang Theory season 10, episode 24 titled "The Long Distance Dissonance," Amy was at Princeton attending its summer program when Sheldon's old assistant Ramona Nowitzki (Riki Lindhome) made moves on him. This had the gang concerned, especially Penny and Bernadette whom Amy specifically instructed to keep an eye on her boyfriend. Penny took it upon herself to straightforwardly tell Sheldon that Ramona is romantically attracted to him — he just hadn't noticed it. However, Sheldon insisted that nothing is happening between them, treating that Ramona is just a "friendly colleague." This left Penny defeated; before leaving her old apartment to go home, she frustratingly told Amy from the painting, which was hung up in its original place setting, that she tried to tip off his boyfriend, he's just too naive to really see Ramona's intentions.
In-between episodes where the painting was featured on The Big Bang Theory, there wasn't any mention of it. Penny never brought it up again, let alone say anything about sneakily moving it back to her old place because frankly, it's not like it will go unnoticed. Amy also didn't change her mind and expressed interest in taking it back, so it's curious how it was returned to its original location. If anything, Sheldon would've at least made a comment about its existence in their apartment considering his penchant for pointing out unusual things.