Step 1: Understanding the Concept
A Graafian follicle has the theca externa, the theca interna and the membrana granulosa around the oocyte.
Step 2: Hormone synthesis
Under LH, theca interna cells make androgens from cholesterol.
Under FSH, the granulosa cells convert androgens to oestrogen (estradiol) using aromatase.
Step 3: Conclusion
The final production of oestrogen is by the membrana granulosa.
Final Answer:
The membrana granulosa produces oestrogen.
\[ \boxed{\text{(A) }\text{membrana granulosa}} \]