You can replace a lost passport much in the same way you acquire a new one. The only difference is that you will need to report the loss and fill out an extra form.
The steps to replace a lost passport are as follows:
Complete Application for New Passport, Form DS-11
Complete Question #18 as follows:
Click here to download Form DS-11
Complete Statement Regarding Stolen or Lost Passport, Form DS-64
You should fill out this form only if your lost passport is still valid. Answer as many questions that you can with as much detail as you can.
Click here to download Form DS-64
Present your forms in person to an acceptance agent.
Along with the two forms above, you will need to take the following items to the acceptance agent in order to replace a lost passport.
If you want to replace your lost US passport in a hurry, you will need to contract a passport and visa expeditor.
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