Thank you - given that her passport is missing and she needs to travel soon, you can apply for an emergency travel document if it is within the next 5 days. She will need to present to her nearest British embassy or consulate, and take with her:
-a completed emergency travel document form (here: https://www.gov.uk/government/publications/application-for-a-united-kingdom-emergency-travel-document--2), -a recent passport photo of herself,
-proof of travel (ie. tickets),
-copy of your and the mother's passport photo page,
-written proof from you and the mother confirming agreement to the application,
The embassy will then assess the application and decide whether she is eligible for one.
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