The wired part (reed switch) should still be fitted to the door frame.
So you should get away with fitting the just the magnet side to the new doors, these could be flush (set into the door) or surface (screwed to the door) either way should be a relatively easy fix.
Have a look on eBay for magnetic alarm door contacts and see which you need.
They are only sold in pairs (switch and magnet) but are only a couple of quid.
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