AnyConnect does not have a max file size limit. It is purely a network adapter which tunnels traffic from point A to point B. The only factor from a networking perspective that could affect this is bandwidth between the client and the headend, though I doubt this would cause that much of a bottleneck.
I'd suggest investigating the customer request closer and looking in to other systems involved with these file transfers.
Sorry we can't be of more help.
Regards,
Luke
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