Yes. An ESTA approval record can be shared with family members or a travel agency.
It is possible to share the approval result or the application status information.
However, ESTA approval is not a separate paper visa or document.
It is an electronic authorization linked to the applicant’s passport information.
For that reason, sharing the approval record does not guarantee entry, and the traveler must use the same passport information connected to the approved ESTA.
Also, even if a family member or travel agency helps with the application, the review is still based entirely on the traveler’s own information.
Therefore, the most important point is not the sharing itself, but whether the passport number, personal details, and application information are correct.