Robert Hooke wrote Letter L-103 to Leeuwenhoek as official notice of his election as member of the Royal Society
This letter has not survived. It is known only by reference in other letters. Hooke dated it 12 April 1680 Old Style, which was 22 April New Style.
The image on the right (click to enlarge) is a detail from Verkolje's portrait of Leeuwenhoek. It has been rotated 90 degrees and shows Leeuwenhoek's hand-written parchment diploma with its red seal. Some of the words are visible. It is the only image of any of the five diplomas that the Royal Society gave out between 1664 and 1680.
There is no mention in Birch, The History of the Royal Society, vol. IV, of Gale’s being charged with the Society’s foreign correspondence.
Hooke’s previous letter to Leeuwenhoek is Letter L-099 of 2 February 1680. Leeuwenhoek responded with Letter L-100 of 13 February 1680 affirming that he would like to be considered for membership in the Royal Society and Letter L-102 of 5 April 1680 about, among other things, the seminal ducts and sperm in the testicle of a rat. Hooke’s next letter to L. is Letter L-112 of 4 July 1681
Letter L-105 of 13 May 1680 to Robert Hooke:
I received your very welcome letter of 12 April O.S., and saw from it that the Honourable members of the Royal Society took great interest in my last observations. Also that you moved my election as a fellow of that Society in its meeting and that I was unanimously elected a fellow. A few days after the receipt of this letter, a box came to hand, enclosing the sealed Diploma, which I beheld affectionately and gratefully.
Letter L-106 of 13 May 1680 to Thomas Gale:
Hooke in his letter of April 12th O.S. tells me that you have taken over the foreign correspondence, and will hence-forward answer my letters.