It is under my impression that interstate and intrastate travel of Helix aspersa is illegal, since they are listed as injurious. However, if you found them in the wild locally, I'm sure they are legal to own. I think only the GALS and GSALS are prohibited to own. Here is a list of what is considered injurious to the state of Florida:
5B-43.003 Snails Injurious to Florida Agriculture.
The following snails shall be considered as injurious to Florida agriculture, and entry into or distribution within the state is prohibited. This prohibition includes live plant-feeding snails in all stages of development, intended for consumption or for any other purpose. Dead, canned or non-living processed snails are exempt from the provisions of this chapter.
(1) Snails.
(a) Achatina spp. (Example: giant African snail).
(b) Helix spp. (Example: brown garden snail).
(c) Theba pisana Muller (white garden snail).
(d) Megalobulimus oblongus (Muller) (giant South American snail).
(e) Any other plant-feeding snail which may be determined by department order or rule to be injurious to Florida agriculture.
Rulemaking Authority 570.07(23), 581.031(1) FS. Law Implemented 581.031(6) FS. History–New 6-15-81, Amended 8-18-85, Formerly 5B-43.03.
Other than this, unless the snail is protected, no permit is needed for intrastate transportation. However, I was advised to only distribute (in this case Zachrysia) to counties that have them.
It is also noted, only certain species are you eligible to get a permit to ship interstate. Here is a PDF of all the states.
www.aphis.usda.gov/plant_health/permits/downloads/snail_matrix.pdf
