I believe it's illegal to put in other public waters (regardless if caught in public or private water). In fact, you can't stock/put any fish into public waters for many obvious reasons (disease, could be new species w no natural predators ect).
I hear of people catching bass from Fork/Hubbard/unameit lake and putting into community ponds or ponds on their land to catch later, all the time. No problem there...
Def need a permit to sell fish...
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Don't worry about the mule, just load the cart