DOS 3.3 to Mac transfer

[Ken Brooks <ken@sparklight.com>]

I picked up an old IIgs because it has a 3 1/2 floppy drive and a 5 1/4
as well.  Aha!  I said, just the hardware I need to transfer all my old
Apple II programs onto modern (Mac) systems, thence to CD and keep
accessible forever.  And, hopefully, run on emulators.

I just spent 3 hours dusting off and bringing up the system.  It boots
from the 5 1/4 just fine, comes up acting like an Apple IIe.  It boots
from the 3 1/2 just fine, comes up in "Finder", reminiscent of the
oldest Mac I ever owned.  

So I try the transfer.  BUT NO!  When I put in my old DOS 3.3 formatted
floppy, it says, "This diskette was formatted for another operating
system and can't be read.  Eject?  Initialize?"

This is Finder 1.2, vintage 1988.  So I'm wondering, is there ANY
version of ANY operating system that will run on a IIgs and let me
transfer old DOS 3.3 disks onto 3 1/2 inch PRODOS format floppies?

(Apart from that I guess I'll have to stick a modem on the IIgs and use
XModem or something to transfer files to a modern system.  Please say
it isn't so!)

Thanks,
Ken