I am very sorry to hear that Jago has passed.
In regards XXXXX XXXXX grieving, there are different opinions on letting the remaining budgie view the deceased one. If Jago died in their shared cage, then I would just leave it at that. Oren will have known even more than us how unwell Jago was. If he was put down at the vets, then I would only say you may show her his body if she appears to be missing/distressed by his disappearance. And she will know what has happened If they were in separate cages, then we'd not need to show her as this could cause anxiety and stress for Oren
In either case, the key approach just now is to comfort Oren, let her grieve and to support her in what will be a tough time for her as well as you. You may find her calling for her mate or looking for him when she is out of the cage. This is ok but when she does so, we want to make sure to be attentive to her. We want to spend more time with her, distract her with play, treats, and toys (try and have at least an hour worth of play sessions throughout the day). Help give her something else to focus on and cope with life without her friend. For this time, you will help fill that void left by her companion.
Overall, Oren was probably aware that her companion was unwell if they shared a cage. If he died in the cage, then she doesn't need to be shown his body. And if was elsewhere when he passed, then showing her isn't necessary unless she is actively distressed by his absence. They key is to distract and divert her attention and support her with your presence while she mourns his loss and cope with life without this former companion.
Please take care,