I doubt it's the fact he used non-synthetic oil that has caused the clutch slip. It's more likely he has used an oil developed for car engines. The majority of car oils contain friction reducing chemicals. Part of the JASO-MA standard is a friction test designed to determine suitability for wet clutch usage. An oil that meets JASO-MA is considered appropriate for wet clutch operations. Oils marketed as motorcycle-specific will carry the JASO-MA label. A properly specified motorcycle oil will still allow for the appropriate lubrication and cooling of a motorcycle clutch, whilst maintaining 100% of the drive to be transmitted by the clutch, even under arduous operating conditions.
Reverting back to the correct oil will not, in my opinion, cure the problem - but I may be wrong! It is likely the clutch plates will have become coated in the friction reducing elements. If it were up to me I would take the clutch plates out and clean them thoroughly at the very least but in reality I would replace them. It's a little like soaking your brake pads in oil - they would never clean up the same again.
What year Suzuki is it? The 1970's aircooled models were a doddle to replace the clutches on. I haven't worked on the watercooled ones but I shouldn't think they are too difficult.
I hope this helps.