Though originally a bit of mid-nineteenth-century American slang for money, this has travelled widely, being cast up on the shores of Britain and Australia among other places. It’s a member of a group of words created in a century-long fit of logographical exuberation which also gave us slumgullion, rambunctious, and absquatulate (not to mention, as Elsie L Warnock did in Dialect Notes in 1913, such lost treasures as scrumdifferous, hyperfirmatious, and supergobosnoptious).
It would seem from the evidence that spondulicks (either so spelled or as spondulix) was originally American college slang. One of its earliest appearances was in a piece about college life in the New York magazine Vanity Fair in 1860: “My friend the Senior got out of spondulix, and borrowed [my watch] to spout for the purpose of bucking the Tiger” (to interpret, his friend had run out of money and pawned the watch to get some more cash in order to gamble on cards, probably faro). The word was used later by such literary luminaries as O Henry and Bret Harte. From usage data, it now looks to be much more common outside the US, to the extent that the New Oxford Dictionary of English marks it as “British slang”.
Where does it come from? “A fanciful coinage”, the Oxford English Dictionary says. It has been described as a “perverted and elaborated” form of greenback (you may feel that to believe spondulicks could come from greenback requires a perverted imagination all its own). Eric Partridge suggests that it might derive from Greek spondulikos, from spondulos, a species of shell once used as money.
However, Doug Wilson pointed out that that Greek stem is also the source of various English words beginning in spondylo– that refer to the spine or vertebrae. He suggested that a stack of coins may have been likened to the spine, with each coin a vertebra. He found a supporting reference in an 1867 book, A Manual of the Art of Prose Composition: for the Use of Colleges and Schools, by John Mitchell Bonnell. A list of provincialisms included: “Spondulics — coin piled for counting”.
If it is indeed college slang, either explanation may well be the kind of academic joke that would appeal. Otherwise, your guess is as good as mine.