Hello!
Rosemow (from sims forum site) advised me to post my feedback about this moving bug here in this post. So here it is! 🙂
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Good day/evening to The Sims forum (and anybody who read it)!
I would like to submit a bug. Was searching on forum/net to see if other players have the same bug or not. There was tooo many post under search "elements" under "bug and gameplay" section, so I post here since this is the closest bug (we can tell the same bug). I have even read crinrict's post" read-first-compiled-list-of-bugs" to look for similar bug too with no luck. But hope somebody who can fix this issue/bug read this post too. 
Ok I stop rambling, here is the issue with Photos
I moved (via phone "move household") my 2 young adult sister sim to a bigger apartment from their old and small one. I did not sell all the furnitures on the moving dialog, since they had too many personal things (like photoes, paintings, collections and my insane alien scientist inventions) to grab one by one into household inventory (hereinafter: HI). They moved in succesfully and I started to grab the items from the HI to redecorate their new flat with all their proudly gathered or handmade collections/items. And when done it, went into live mode (since in buildmode not able to drag and drop into storage/elemental display rack) to put the element into the rack. I could not grab and put it (in live mode) because it was grayed out saying my sim does not have it. But she already collected it and it is in collection panel too. She had an other one in her personal inventory (hereinafter: PI) too which works perfectly but those which was in the display rack and went into the HI during moving.
And then I remembered that I had a few items in the storage chest too, all of them gone and even the treasure chest is broken too. I could not put anything new item into that chest either. So all the items which was in chest gone too and the chest broken too. Luckily I stored there just duplicates which was already in PI/HI or in the rooms. Anyway I have the save file too if need.
Oh I was curious if i redo the HI moving (with keep furniture -hereinafter: wkf) will it happen the same way. Tried it and those items was broken too. Then I tried if in live mode with my sims grab items from the rack into her PI with "put in inventory" and then put on ground. Moved my sims via phone to an other flat wkf option. All collections was broken with gray "put in inventory". Then was thinking which option is the bugged one: the keep furniture or the HI cause the bug. So I did "two bird with one stone" method. I put 2 item (xenopetrium and live space porcupine) into HI manually then move out wkf option. All the collectible which got in HI wkf option bugged but those which put in HI manually. So something happens when the game put all items into HI during wkf option cause the gray "put in inventory" syndrome bug.
I have mods (just default skin/eyes, one hair recolour and lashes/makeup) but those should not cause this bug.
I'm not sure maybe it was in sims 3 when put the treasure chest into HI and then put back after moving and all the items stayed and worked perfectly or it was in sims 4 too and then something happened and broken. Maybe in sim 4 worked too in early times since I used a lot of time the treasure chest item to save the PI and HI and don't remember if stumbled across this bug before. Just the moving break the storage chest ( I have tried if I just put the chest into the HI and then change to play mode and then back to build mode and the chest was working well with all the items in it).
To get back all my items to work correctly I had to choose a cheat method with buydebug. I put all items (which was broken coz of the wkf option) on the ground and type in search line those names and bought them in buy mode and replaced them. So I did not have to find them in world again since they were already in the collection panel. Now I have a working collectibles.
In future I will remember to put all the collectible items manually one by one and not use the wkf option.
So in short word: keep furniture option breaks the HI items during moving. So If You want to use all collectibles with your Sims and want to save time (to recover all items one by one) then put them all manually into ur HI or PI before move out and get out all your items from storage chest too. A painful solution in my oppinion (since keep furniture option is soo good thing during moving especially when you have sooo many completed collection like my old household which is full of dust in my backup folder) but still not as painfull to recover all items one by one in buydebug cheat search panel. I hope one day it will be fixed. Im curious what story will they write into patch note when they fix it. haha would be funny to read the typical dialog for this bug. 
P.S.: sorry for long post
Sincerely, Trillian 
Dag-Dag!
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Have a nice weekend 🙂