There had been societies of painters earlier in Britain, but it wasn’t until 1768 that British artists formed themselves into the Royal Academy of Arts. At a time when women were excluded from so many organisations, one surprising feature of the new Royal Academy was two founding women members: Angelica Kauffmann (or Kauffman) and Mary Moser.
Angelica Kauffmann, who was originally Swiss, enjoyed meteoric rise to fame, and remains quite well known, yet Mary Moser has been all but forgotten today, and her paintings have almost vanished. Moser had an eminent career, and died on 2 May 1819, the three hundredth anniversary of Leonardo da Vinci’s death.
Mary Moser was the daughter of another Swiss-born artist, and was born in London on 27 October 1744. She benefitted from precocious talent and the early training of her father, resulting in winning her first medal from the Society of Arts when she was only fourteen. She is recorded to have exhibited floral paintings and a few history paintings at the Society of Artists of Great Britain in the following years.
In 1768, together with her father and Angelica Kauffmann, she was one of the thirty-four artists who founded the Royal Academy of Arts in London. She took an active role in the Royal Academy’s proceedings in subsequent years. Moser, then only twenty-four, was also the youngest of the founding members.

For most of her career, Moser painted portraits, such as this of Joseph Nollekens from 1770-71, who was the finest British sculptor of the time, and floral still lifes.

This arrangement of Flowers, Still Life dates from about 1780.

The collection of the Royal Academy in London holds two paintings of hers, both donated by the artist. This is Spring from about 1780.

This is Summer from about the same date.
At some time in the 1780s, Moser was appointed drawing mistress to Princess Elizabeth, and in the 1790s she completed a series of royal commissions, including one for the floral decorative design of a room in Frogmore House, Windsor, for Queen Charlotte, wife of King George III. The latter work included a combination of large canvas paintings by Moser and painted walls, to create the illusion of “an arbour open to the skies”, and is the most substantial memorial to her work remaining.
In 1793, when she was forty-nine, Moser married for the first time. She continued to paint and exhibit at the Royal Academy until her eyesight failed in 1802, then became more involved in the running of the Royal Academy, until her death in London on 2 May 1819, at the age of 74.

The only portrait that I have been able to find of her is this, by George Romney, painted in about 1770-71.
After Mary Moser and Angelica Kauffmann (who died in 1807), the next woman to be elected a full member of the Royal Academy was Dame Laura Knight, in 1936. For well over a century, not a single academician was a woman.