Unfortunately, unless the application explicitly supports it, you need to write a program to do it for you. See the end of this answer for why.
What you can do, however, is get a program to simulate/script keystrokes and mouse movements. Record yourself going through each box, copying and pasting it into the different window, and playing back the macro at a very high speed. You can also use AutoIt (link above) to move data directly to/from window controls (e.g. textboxes), which would be a lot faster then even using the clipboard.
The AutoIt distribution includes software to reveal window controls from arbitrary applications (it's called the AutoIt Window Tool) to assist you with determining the window control names. AutoIt can directly access the values of these controls, and modify them if possible. It would be trivial to write a script to move data between two selected instances of a program.
The reason that you can't do this natively is, firstly, you cannot select multiple textboxes at once. While it is possible to program applications to insert data directly into the clipboard, the program would have to support this. Secondly, if you did copy all the data to the clipboard, unless (again) the application supported pasting to multiple textboxes at once (meaning it was specifically programmed to do so), it wouldn't know where to split the data.