Based on a quick comparison I don't see why not from a strength standpoint given the Rigby's significantly lower pressure. Body taper and length is close enough you might not even have to mess with the magazine to get it to feed. Overall length might be the limiting factor - not sure how much wiggle room is left in the magazine or bolt throw of the .338 Lapua, but we're only talking a fudge over 1/16" difference.
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