I think when you delete a file over the network, it's gone. I don't think it goes in the recycle bin of either computer.
You could try running a data recovery program like Recuva on the system it was deleted from. It may still be available if it's drive space has not been over written.
My Computer
Computer type
PC/Desktop
Computer Manufacturer/Model Number
Lenovo IdeaCenter 450
OS
Windows 10 Pro X64
CPU
Intel Quad Core i7-4770 @ 3.4Ghz
Memory
16.0GB PC3-12800 DDR3 SDRAM 1600 MHz
Graphics Card(s)
Intel Integrated HD Graphics
Sound Card
Realtek HD Audio
Monitor(s) Displays
HP 22" LCD
Screen Resolution
1680 x 1050
Hard Drives
250GB Samsung EVO SATA-3 SSD
2TB Seagate ST2000DM001 SATA-2
1.5TB Seagate ST3150041AS SATA
System Restore does not save user files, only system files so it will never be of any use for problems like this. Spend some time and money and setup a good backup strategy, you won't be sorry.
My Computer
Computer type
PC/Desktop
Computer Manufacturer/Model Number
Lenovo IdeaCenter 450
OS
Windows 10 Pro X64
CPU
Intel Quad Core i7-4770 @ 3.4Ghz
Memory
16.0GB PC3-12800 DDR3 SDRAM 1600 MHz
Graphics Card(s)
Intel Integrated HD Graphics
Sound Card
Realtek HD Audio
Monitor(s) Displays
HP 22" LCD
Screen Resolution
1680 x 1050
Hard Drives
250GB Samsung EVO SATA-3 SSD
2TB Seagate ST2000DM001 SATA-2
1.5TB Seagate ST3150041AS SATA