But do they actually have the right to be there originally ?
IIRC, the islands were uninhabited until the French set up a naval garrison there, in the 1700s.
Which Britain kicked out, within a year.
Argentine occupation of the islands can be measured in weeks, unlike the UK's centuries. And none of it until the French and British had been there first.
Not saying right or wrong; just that "first dibs" gets Argentina nowhere, as a basis for any claim.
(The islands are also over 300 miles from the coast of Argentina; and a sparsely-inhabited part of Argentina, even now, at that. I doubt that the Argies even knew they were there, for most of their history).