Perfectly beautiful English!
She had a laparoscopy last May and last June. So then,
she had had two prior laparoscopies prior to being admitted to (the) hosiptal.
The underlined bit identifies the event that happened 1st.
When speaking about two connected events in the past, use the past perfect 'had + main verb' to express the event that happens first, and use the past simple (main verb) to express the event that happens next.
I had eaten half the dog before the pizza arrived!![]()
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