Checking the movement of travellers at all possible entry points into the EU is a very complicated undertaking. There are not only cars on roads, Ships and Planes but also travelers on foot who try to cross frontiers at any point where this is possible !
Are there foolproof checks at ALL crossing points into or out of the EU of every traveller ? This is doubtful.
Are there inter-linked computers where all the information of movements is stocked and available for cross-checking purposes and for investigations ?
The problem is complex and provokes the question whether there should not be checks on migrants inside the EU : high quality false documentation can be ordered on the black market according to reports !