Is it permissible to falsify a vaccination certificate for Hajj while in a foreign country, knowing that the vaccination is administered in Jeddah, and is this Hajj valid?

The basic principle is that forging certificates is forbidden because it involves lying, betrayal, and deception. However, if a person is compelled to do so, for example, if their obligatory Hajj depends on this forgery and they cannot obtain a genuine vaccination certificate, then there is no harm in forging it, especially if they will be vaccinated later. And the Hajj will be valid, God willing, even if the forgery was forbidden.