You asked us not to recommend the obvious, and thus I won't ...
Adobe InDesign and Adobe Illustrator were designed to be complementary, but certainly not to be interchangeable. InDesign's forté is layout while Illustrator seriously excels at complex illustration. Typically Illustrator content is placed into InDesign (normally as PDF) when the graphic requirements exceed the already ample capabilities of InDesign. Illustrator is most often the choice of packaging professionals because of its ability to handle exceptionally complex designs. And many printing companies that specialize in packaging print such packaging directly from Illustrator, either with or without an intermediate PDF file. SInce you client has chosen a printer based on ability to print packaging, that is probably the reason for the request for Illustrator files.
Unfortunately for you, there is no simple way of doing what you want other than placing the 52 pages of PDF exported from InDesign into the comparable “pages” in an Illustrator document's artboard. (Note, you had better check with the Chinese printer. They may actually want 52 separate Illustrator files and in a format of a much earlier Illustrator release!)
Another thing to consider is to contact the Chinese printer's CSR directly and explain your situation. Maybe for non-packaging content that doesn't need to concern itself with folds, varnishes, die cutting, etc., a properly-created PDF/X-4 file may be all they really require. Doesn't hurt to ask!
That's pretty much as I thought, but best to check eh? Luckily the printer as agreed to accept just the PDF for the leaflet, I didn't fancy starting that all over again!