Answer
Yes. It is better to order duplicate birth, marriage, divorce, and name-change certificates from the civil registry office before departure and prepare them for use abroad. After moving, it can be difficult to obtain the necessary certificates from Russia.
An old original document from home is not always suitable: it may be damaged, laminated, difficult to read, or unsuitable for apostille. A duplicate is easier to correct and certify while the person is in the country of issue.
It is especially important to have a continuous chain of surnames. If, after moving, it turns out that a marriage, divorce, or name-change record is missing, obtaining it through a consulate, an interstate request, or a representative will take longer. Therefore, it is better to prepare basic duplicates in advance.