so something has gone away in the real world, and rather than just deleting it from OpenStreetMap, you’d like to move it to OpenHistoricalMap.
That’s a great idea, but don’t rush.
OHM has a mixed licensing philosophy. The license tag should be set on entities in the DB (high level relations or ways, no need to tag everything). Using CC0 (about the same as Public Domain) is preferred. Somethings may be licensed CC-BY-SA.
Because of this, there are steps you need to take.
First you need to examine the history of the object and find out who edited it (could be more than one person). Sometimes you’re fortunate and there is only one editor, which makes it easier. You will need to reach out to them, probably using the OSM messaging system, to find out if they object to their work being moved. Be respectful and nice, and explain clearly what you are doing. Emphasize that yorr goal is to preserve their work. Explain that it will need to be relicensed, preferably under CC0 (failing that, CC-BY-SA). You will find that many (most?) mappers are happy with this and will grant permission.
You will then need to hone your map editor skills, exporting the .osm file from OSM and importing it to OHM. Do not forget to add the extra OHM tags - license, source, start & end dates. Make sure you give credit.
Some things may be approached differently. For example, you may find that something predates the license change. In this case, it may well be available from the planet at fosm.org. If, for example, it is unmodified TIGER then it was originally public domain and is up for grabs. But if it’s unmodified TIGER, there is a fair chance an improved copy exists on the Census Bureau website so consider sourcing it there.