The 1879 reference goes into more detail:
Journal of Horticulture, 37:147-148 (1879)
ROSE SOUVENIR DE LA MALMAISON.
M. Beluze, sen., Rose-grower at Lyons, sowed in the year 1840 a number of seeds which produced the magnificent Rose under consideration. Two years later the raiser was in a position to affirm that something very exceptional had come to light, although at that time he had but one flower, and that one the solitary shoot of the parent plant itself only 13 inches high. This acquisition was brought under the cognisance of the distinguished rosarian M. Plantier, who at once pronounced it to be the best introduction of the times. The flower is distinguished by its rare perfection of form and colouring, yet the first flower was but little over an inch in diameter; but when buds were inserted on strong Bengal stocks the result was natural-sized flowers averaging 3 inches in diameter. That was in the year 1843, the year it was sent out. The most important question, however, was to determine of which variety the seeds which produced this flower were saved. After several delays the Horticultural Society of the Rhone convened several meetings to take this matter into consideration, and ultimately came to the following conclusion: That as seeds of Roses are, except in rare instances, not sown as so many different varieties, it follows that each pan contained the seed of one class. It is therefore not quite certain, though extremely probable, that Souvenir de la Malmaison is the offspring of the Bourbon Rose Madame Desprez; and that is the opinion of the raiser himself, further strengthened by M. Plantier.

If this assertion requires further proof it will be found in the fact that nearly all the seeds gathered and sown came from Madame Desprez, and it will be found upon careful examination that there is a great similarity of habit and foliage between the two varieties. The Bourbon Roses Jaquard [Jacquard], Cendres de Napoleon, Etoile du Berger, raised previous to Souvenir de la Malmaison, are all the offspring of Madame Desprez. The parent plant of Souvenir de la Malmaison still exists at Lyons, where it continues to flourish in spite of being cut down for propagation and growing in a position not at all favourable to it—that is, facing the south. Still growing against the wall where it was first planted out in 1841, this knotty old lady, whose children are to-day distributed throughout the world, still blooms very abundantly, notwithstanding that she had to endure the hardest winters and such severe gales that everything was swept away except one or two eyes at the base.

Souvenir de la Malmaison, with its great massive flowers, white slightly diffused with flesh colour, of admirable form, will always retain the exclusive privilege of being a gem of the very first water, esteemed and sought after by the lovers of Roses of all nations, who continue to find in this remarkable variety a full supply of suitable Roses which help to enrich the choicest bouquets at all seasons—(Journal des Roses.)