Is the gray "hook" an original LEGO item? Please see the red plate for size comparison.
This looks to be Arm Piece with Towball and Clip.
There are quite a lot of copycats these days. So there is always a chance it is clone piece. To confirm this is genuine LEGO piece best thing would be to look for LEGO logo, but it is not always available on small pieces. Alternatively you can look for "30082" which is a part number.
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yep, that's the one. thanks! I am pretty sure it is genuine because it came with an old set which did not seems to be contaminated with modern fake parts – fabian Feb 1 '19 at 17:52
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1It is quite versatile part since there are at list 3 ways to connect it: 1) using the clip; 2) the towball; 3) the whole in towball (for a rope). There might even be 4th one - the bar between clip and ball, but I'm not sure it is wide enough for another part with clip. So there are many ways to use it. Do you happen to know which set this part came with? – Alex Feb 1 '19 at 18:00
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in this case it appears in sets 6544 and 6339 - the space shuttle with plane or lunch pad. it is holding a satelite in the cargo bay of the shuttle – fabian Feb 4 '19 at 11:02
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apologies, this is not the piece on those shuttle sets, it is item number 3614b – fabian Feb 7 '19 at 12:28