Yes, but member states tried to sack her two days prior to the Brexit date on the basis that the UK would be out of the EU and as such anyone appointed to the EU, by virtue of UK membership, would also be out of a job.
She has a mandate until Oct 21 and has UK and Luxembourg nationality.
The President of the ECJ, on Brexit day indicated her vacancy and asked 27 member states to nominate someone to fill it.
But, she's not a judge, she's an advocate General and her job is not attached to any particular member states, regardless of who nominated her.
The court determines if the role ends prematurely, not a decision by the President on the assumption of departure. She asked for it to be referred to the court for decision, based upon Art.50 but it was refused.
It's unfair and petty.