Summary
Briefcases exported from Web Access have a .zip file extension instead of .lfb. Web Access will recognize that the file is a Laserfiche briefcase if you attempt to import it through Web Access. However, the Laserfiche Client will not automatically recognize the file as a Laserfiche briefcase and will not import it as a Laserfiche briefcase.
Workaround
Rename briefcases exported from Web Access to have a .lfb file extension before attempting to import it through the Laserfiche Client.