Lawsy! It's turned into a weed, Weziwe? The safest way involves hard labor and organic pre-emergent:
Most kinds should be easy enough to dig up. Though labor intensive over large areas, the root crowns don't usually go deep, and the roots themselves don't sprout without an attached crown. Regular followup applications with corn gluten meal may be necessary for a few years to keep the seeds from sprouting.
The next step up would be to use a glyphosphate product to kill the growing plants (not effective without green foliage) and a product containing benefin as a pre-emergent afterward. Unfortunately, that's much more toxic to the environment and applicator, both. Definitely avoid soil sterilants like prometone, pyrosulfatole, or polyborochlorates, since they will effectively kill the soil for the next 5-20 years.

Golly, Tugbrethil! I thought Weziwe wanted to send Alstroemeria by post or courier!

Well you guys, I came on to say to Weziwe, did you mean despatch as in post somewhere, or did you mean despatch as in killing... could be either.

Ouch! I didn't think about shipping. I don't have much experience with that, but I know a few of the critical parameters. The roots don't like to stay out of the soil long, so they should be planted within a week or two of being dug up. It is also too easy to break the tuberous roots from the root crowns, which will then sprout weakly, if at all. Care will be needed in digging them up and packing them, and the recipient will need to unpack and plant them very carefully. It may be safer to carefully start them from locally dug roots in pulp pots, let them get established, and ship them in the pots during the normal dormant season. Much easier to ship and start seeds than roots, though that doesn't allow for clones.