It is possible to enucleate a cell (ie. suck out the nucleus) and replace it with an exogenous nucleus from another cell. After all, this is the basis of cloning by nuclear transfer – fuse a donor cell (with donor nucleus) to an enucleated ovum. But that’s different to the hypothetical scenario being posed by the article. The guy in the article is suggesting that we can somehow insert his reconstituted in vitro DNA into a nucleus. He could try to inject it directly into the nucleus of a mouse cell but how would he first remove all the mouse chromosomes? And that brings up another glaring problem with the whole idea. Performing mutagenesis to convert human DNA into Neanderthal DNA, then stitching together all the fragments, is done on naked DNA. How does this guy propose to somehow convert his naked DNA into functional chromosomes that can be packaged into a nucleus? I guess that would be something along the lines of transferring a nucleus from the ovum of the patient into an enucleated donor ovum which still contain their mitochondria (without the mutation in question).