Thanks , I was looking at just filling that gap with perhaps some product / mud or cement and maybe somehow creating that similar oatrenr by sponge or a bag. It doesn't have to look exactly the same.Yes it can be repaired.
First before I did Stucco matching look into the possibility of pulling the box off the wall about 1" and putting a wood backer in that is 2.25" larger than the box & placing a sealant between the board & the Stucco & reattach the box.
To repair the Stucco you will need a Cement- Lime based mix to fill the area leaving about 1/8" shy of the existing finish.
To match the Stucco texture mix a soupy mixture of the cement material & dash it on the repair area the closer you are to the substrate the larger the bumps will be to get smaller move back.
Make sure to tape off the box & the area around the repair.
When the repair is complete BUT still workable remove the tape a brush the edges off.
Also keep in mind that Stucco is cement & will not adhere to the painted area.
For a patch that size drive around locally in your area you should find many ongoing Stucco job sites stop by & explain what you have to repair, most if not all will give you that small amount of the products required to complete the patch work. They may also have a Synthetic Stucco product on site that will go over a painted surface.