The system, installed in the G3 clamshell iBook, likely won't
run correctly if at all, if copied or cloned into an iBook G4.
The actual installer DVD or CD puts in items hardware vintage
specific, so if a retail disc were used in the Clamshell, the
resulting system would not be correct for a later iBook G4.
Or not likely.
However you could try to call AppleCare or Sales Support
(not online store, or retail) to get a Replacement Installer
DVD with white plain label, of Tiger OS X 10.4. That may
not be old enough, however, since some of the Clamshell
models topped out at Panther 10.3.9 or use installer CDs.
If the Clamshell has FireWire ports, that is a workaround
if its optical drive cannot use DVD installers, since an
iBook G4 has FW400 ports and could be used in Target
Disk Mode as an optical drive for the older G3 iBook.
You could research the correct original install-restore CDs
for the vintage iBook G3 Clamshell to see if you could get
the original part numbers for that vintage.
An independent Apple Specialist tech may have a way to
install a test system on an older iBook G3, but that software
is not something most would bother with due to the age
and unlikelihood of much demand. So you may be looking
at second hand stores, moving sales, craigslist ads, ebay
and/or amazon affilate stores online to sleuth out installers.
And OS X does not copy, it must be installed, or if you had
the exact same duplicate computer and a system clone,
the installed version (or Target Disk Mode in the other) may
be used to attempt to make a boot clone, to test/repair the
other similar computer. The jump from an early G3 to later
G4 is not a likely match, and the license for each system is
required to have the original or retail install discs as proof.
Unless you had an original 'family pack' retail install disc set.
Good luck & happy computing! 🙂