Fluid product dispenser

A method of assembling a fluid dispenser comprising:

• a fluid reservoir including a neck that defines a constricted opening that communicates with an inside volume of greater size;
• and
• a dispenser member, such as a pump or a valve, including a fluid inlet that is provided with a dip tube;
• a substantially-plane flexible sheet having shape memory, the sheet extending along a dip tube and being fastened to the dip tube, the sheet presenting a transverse dimension, in the direction that is perpendicular to the dip tube, that is greater than the dimension of the constricted opening, such that the sheet must be caused to take up a deformed configuration in order to pass through the neck, and must then relax into a substantially-plane rest configuration inside the inside volume;
• the method being characterized in that the sheet presents a bottom edge having a portion that defines a bottom point that is situated at the dip tube, the bottom point and the dip tube being positioned in the opening, with the sheet in the rest configuration so that, in said rest configuration, the portion penetrates into the constricted opening in such a manner as to initiate the deformation of the sheet, so as to bring it subsequently into its deformed configuration.