The easiest way is to install WinFrotz or one of the other terps, but if you want to continue using DOSBox:

First, you're going to need to edit the desktop shortcut. If you've let the installer generate one, right click on it and select Properties. Go in and remove the bit that says

-c "exit"

at the end of the Target line. Click Apply and then OK. Next pop into the subdirectory for Zork I (default Program Files\Zork Anthology\Zork) and open dosboxZork.conf for editing in Notepad or something similar.

Go all the way to the bottom of the file and remove the last three lines - get rid of:

nnansi.com U
cls
exit

Then save your changes and quit. Next time you open the shortcut for the game, when you finish it, it'll drop you to DOSBox's DOS prompt, letting you read the last of the text. You'll have to type "exit" to quit DOSBox each time you play, but that's a small price to pay.

Follow this procedure for each of the game titles (except Zork Zero and Beyond Zork, which just need to lose the last two lines and the -c "exit" from their shortcuts, plus those two might let you 'press any key to exit' before dropping you to DOS), and bob's your uncle!

Couple caveats, though. DOSBox doesn't have a scrollback as far as I know, so if the game ends with a big ole infodump the first part may still scroll by. As far as saves go, I don't think they're portable... unless you're using a modern terp, in which case Quetzal is the save format they obey.