E-cigarette rechargeable battery charging case comprising: > a base comprising a first recess for receiving an e-cigarette rechargeable battery, > a cover, o covering said first recess when in closed position, o making said first recess accessible when in open position, > a flexible hinge linking said cover to said base, o a first extension of said hinge being fastened to cover structure, o a second extension of said hinge being fastened to base structure, ▪ wherein said second hinge extension: • is tightened between tightening parts (45, 15) of said base structure, characterized in that: ▪ said second hinge extension: • cooperates with at least an aligning part of base structure, o so as to align said base and said hinge with respect to each other, • and is tightened between tightening parts (45, 15) of said base structure, o so as to maintain aligned said base and said hinge with respect to each other, over time, despite successive openings and closings of said cover. > a base comprising a first recess for receiving an e-cigarette rechargeable battery, > a cover, o covering said first recess when in closed position, o making said first recess accessible when in open position, o covering said first recess when in closed position, o making said first recess accessible when in open position, > a flexible hinge linking said cover to said base, o a first extension of said hinge being fastened to cover structure, o a second extension of said hinge being fastened to base structure, ▪ wherein said second hinge extension: • is tightened between tightening parts (45, 15) of said base structure, characterized in that: ▪ said second hinge extension: • cooperates with at least an aligning part of base structure, o so as to align said base and said hinge with respect to each other, • and is tightened between tightening parts (45, 15) of said base structure, o so as to maintain aligned said base and said hinge with respect to each other, over time, despite successive openings and closings of said cover. o a first extension of said hinge being fastened to cover structure, o a second extension of said hinge being fastened to base structure, ▪ wherein said second hinge extension: • is tightened between tightening parts (45, 15) of said base structure, ▪ wherein said second hinge extension: • is tightened between tightening parts (45, 15) of said base structure, • is tightened between tightening parts (45, 15) of said base structure, ▪ said second hinge extension: • cooperates with at least an aligning part of base structure, o so as to align said base and said hinge with respect to each other, • and is tightened between tightening parts (45, 15) of said base structure, o so as to maintain aligned said base and said hinge with respect to each other, over time, despite successive openings and closings of said cover. • cooperates with at least an aligning part of base structure, o so as to align said base and said hinge with respect to each other, o so as to align said base and said hinge with respect to each other, • and is tightened between tightening parts (45, 15) of said base structure, o so as to maintain aligned said base and said hinge with respect to each other, over time, despite successive openings and closings of said cover. o so as to maintain aligned said base and said hinge with respect to each other, over time, despite successive openings and closings of said cover.