The child table above CANNOT possibly have two records with the same autonumber, 5. Access will not allow duplicate autonumbers in a table. Also, a table is allowed only ONE autonumber FIELD to be defined.
So it's murky to me just how your tables are designed. I have never seen foreign keys defined as autonumbers, and can't imagine how that could work.
The child table links (foreign keys) pointing back to the parent CANNOT be an autonumber in the original tables. As stated, autonumbers cannot be dictated. Those links in the child tables have to be Long Integer and will not change when archived or restored.
Without seeing your relationship diagram, I don't understand the function of the autonumber (not the links back to the parent, these are traditionally called Foreign Keys) fields in the child tables at all.
One way of achieving you goal with safety without manipulating the keys:
Copy the entire database as a duplicate with a new name.
Open the new database and delete all the child records that you want to keep in the original. Delete all the parent records that you want to keep in the original. This will leave you with only the records you want archived.
Then
Open the original database and delete all the child records that you wanted archived. Delete all the parent records that you wanted archived.
Now you have two guaranteed working databases, one with active records and one with archived records.
Another approach:
When archiving, only archive the child records. Do not archive parents.
Then restoring a child record is simply a matter of appending it back into the original. It will attach to the existing parent. This can only work if the foreign keys in the child records (the pointer back to the parent) are long integers (as it should be).
This is the simplest way, and the method I would use. Tradeoff is that Parents remain in original even if they have no children. You would have to decide if this fact would present problems.
More:
I think you might be confused about the one-to-many table setup in Access, and about the function of primary keys, autonumbers and foreign keys.
Have a look at this video. The words "Foreign Keys" are not mentioned until near the end, so be sure to stay tuned for the full 10 minutes.
4. Microsoft Access 2016 Basics: One To Many Relationships - Bing video