Assembly comprising a substantially tubular intermediate attachment part with a first through-passage for attaching a screw-through dental prosthesis component or a dental tool to a dental implant, said intermediate attachment part extending along a first longitudinal axis (I-I) between a first end and a second end, and in which: - the first end comprises a first set of longitudinal fins (8a-8c), each longitudinal fin (8a-8c) comprising a free distal portion (80a-80c) that can move radially in an elastic manner in order to engage by snap-fitting in the dental prosthetic component or in the dental tool, - the assembly comprises a dental implant extending along a second longitudinal axis (II-II) between a proximal end and a distal end, with an interior connection housing extending from the distal end and toward the proximal end and comprising an internally threaded proximal segment, - the assembly comprises an attachment screw comprising a screw head from which there extends a screw shank equipped with a threaded segment intended to be received by screw-fitting in the internally threaded proximal segment of the dental implant, characterized in that: - the second end comprises a second set of longitudinal fins (9a-9c), each longitudinal fin (9a-9c) comprising a free distal portion (90a-90c) that can move radially in an elastic manner in order to engage by snap-fitting in the dental implant, - the first and second sets of longitudinal fins (8a-8c; 9a-9c) are defined by a plurality of longitudinal slots (F1-F6) extending over just a portion of the length of the intermediate attachment part and originating alternately from the first end and from the second end, said slots (F1-F6) extending along the one same intermediate axial segment of the intermediate attachment part such that the longitudinal fins (8a-8c; 9a-9c) of the first and second sets exhibit an overlap along their length, - the internal connection housing comprises a first groove, formed between the internally threaded proximal segment and the distal end of the dental implant and intended to accept by snap-fitting the free distal portions (90a-90c) of the fins (9a-9c) of the second set of longitudinal fins (9a-9c). - the first end comprises a first set of longitudinal fins (8a-8c), each longitudinal fin (8a-8c) comprising a free distal portion (80a-80c) that can move radially in an elastic manner in order to engage by snap-fitting in the dental prosthetic component or in the dental tool, - the assembly comprises a dental implant extending along a second longitudinal axis (II-II) between a proximal end and a distal end, with an interior connection housing extending from the distal end and toward the proximal end and comprising an internally threaded proximal segment, - the assembly comprises an attachment screw comprising a screw head from which there extends a screw shank equipped with a threaded segment intended to be received by screw-fitting in the internally threaded proximal segment of the dental implant, - the second end comprises a second set of longitudinal fins (9a-9c), each longitudinal fin (9a-9c) comprising a free distal portion (90a-90c) that can move radially in an elastic manner in order to engage by snap-fitting in the dental implant, - the first and second sets of longitudinal fins (8a-8c; 9a-9c) are defined by a plurality of longitudinal slots (F1-F6) extending over just a portion of the length of the intermediate attachment part and originating alternately from the first end and from the second end, said slots (F1-F6) extending along the one same intermediate axial segment of the intermediate attachment part such that the longitudinal fins (8a-8c; 9a-9c) of the first and second sets exhibit an overlap along their length, - the internal connection housing comprises a first groove, formed between the internally threaded proximal segment and the distal end of the dental implant and intended to accept by snap-fitting the free distal portions (90a-90c) of the fins (9a-9c) of the second set of longitudinal fins (9a-9c).