Assembly comprising: - a connecting member capable of being mounted on a first collar defining an opening of a first medical container, said first collar having an outer diameter D1, said connecting member having an axial through hole for access to said opening of said first medical container, said connecting member having an outer diameter D2, with D1 strictly less than D2, - an adaptor comprising: o a gripping member capable of being laterally mounted on either said connecting member or on a second collar defining an opening of a second medical container, said second collar having an outer diameter D2, said gripping member having a central hole for access to said opening of said second medical container, o a pierceable elastomeric piece, fixed with respect to said gripping member, arranged so as to face said through hole or central hole when said gripping member is mounted on said connecting member or on said second medical container, characterized in that, - said connecting member being capable of being axially mounted on said first collar defining an opening of a first medical container, the assembly further comprises: - a protecting envelope comprising a rigid shell substantially surrounding said connecting member and said adaptor in a storage position of the assembly, in which the connecting member is separate from the adaptor, said rigid shell being closed by a removable film, - wherein said assembly further comprises temporary fixing means (27; 55) for preventing said connecting member from escaping from said rigid shell when said film is removed. - a connecting member capable of being mounted on a first collar defining an opening of a first medical container, said first collar having an outer diameter D1, said connecting member having an axial through hole for access to said opening of said first medical container, said connecting member having an outer diameter D2, with D1 strictly less than D2, - an adaptor comprising: o a gripping member capable of being laterally mounted on either said connecting member or on a second collar defining an opening of a second medical container, said second collar having an outer diameter D2, said gripping member having a central hole for access to said opening of said second medical container, o a pierceable elastomeric piece, fixed with respect to said gripping member, arranged so as to face said through hole or central hole when said gripping member is mounted on said connecting member or on said second medical container, characterized in that, o a gripping member capable of being laterally mounted on either said connecting member or on a second collar defining an opening of a second medical container, said second collar having an outer diameter D2, said gripping member having a central hole for access to said opening of said second medical container, o a pierceable elastomeric piece, fixed with respect to said gripping member, arranged so as to face said through hole or central hole when said gripping member is mounted on said connecting member or on said second medical container, - said connecting member being capable of being axially mounted on said first collar defining an opening of a first medical container, the assembly further comprises: - a protecting envelope comprising a rigid shell substantially surrounding said connecting member and said adaptor in a storage position of the assembly, in which the connecting member is separate from the adaptor, said rigid shell being closed by a removable film, - wherein said assembly further comprises temporary fixing means (27; 55) for preventing said connecting member from escaping from said rigid shell when said film is removed.