Lifting a engineered oak wood flooring?

It is possible to lift t/g glued engineered floor but great care would to be taken so you do not damage the tongues of the boards. As far as fitting them back together, you would need to use a router with the correct routing bit (to fit the groove), and clean all the old glue out of the groove. Then I would suggest using a sharp chisel and hammer to clean the tongue, allowing you to glue the floor back together. This method is very time consuming and wouldn't be cost effective to pay someone to do this - you will also need a lot of patience and take great care when clean the tongues/grooves - this is not an easy job! In my opinion, it is only ever worth doing when you do not have any other solution - or the wood is worth the effort ie extremely rare, worth renovating. I'm sure other fitters will make other suggestions, but this is from my own experience as a fitter of many years.