The archeological reassembly of ruined monuments from fallen or decayed fragments (incorporating new materials when necessary) WordNet 3.0 & Open English WordNet

Anastylosis is an architectural conservation term for a reconstruction technique whereby a ruined building or monument is restored using the original architectural elements to the greatest degree possible, combined with modern materials if necessary, ensuring that the latter are unobtrusive while clearly recognizable as replacement materials. Wikipedia

reconstruction of archeological ruins using their original materials Wikidata

The reassembly of ruined monuments or other artifacts from remaining fragments in an archeologically responsible way (with use of modern materials when needed). Wiktionary

Reassembly of ruined monuments. Wiktionary (translation)