Yes, but the UK taxpayer over 8,000 miles away has to pay millions of pounds each year for their defence. I do not mean an immediate handover but something much more like the Good Friday agreement in Ireland that would happen over a long period of time.
For example:
"McSmith reports that the military in the area will cost the UK £61 million ($96 million) in 2012-13, which is expected to increase by £2 million ($3.14 million) each year.
While in the grandiose world of military budgets that might not be that much, when you look at the cost per British citizen on the Falklands, it works out at more than a whopping £20,000 or $31,000 (and that is only the defense budget, other costs will be born on other budgets)."
https://www.businessinsider.com/falkland-islands-cost-2012-2?r=US&IR=T
The UK should never tolerate an aggressive invasion by a hostile fascist dictatorship/junta, but should look at working with a peaceful democracy for a long term solution. We also have a contracting military and there in the future may come a point where we are no longer able to defend these islands.