Spoilers below
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First, after Tamra Train arc, Braun short of kidnaps Soleum (he kinda agrees to it but well... corruption) and then Braun have this live talk show and Soleum works with him there for 1 month, after that Soleum is somehow rescued and kinda promises that he will get a new doll and summon Braun again as a friend, which Braun is in agreement. It takes some time but Soleum goes to the Theme Park to fulfill his promise and get a new doll, it works somehow and Braun becomes once again a Good Friend Doll.
As for the coin he used as plant, it only copies the "dna" information and creates a brand new item so the coin that is the especialized equipment isn't the same inside the doll, but a new one created by the machine after scanning Chief Lizard equipment, the silver coin and Kim Soleum himself.
Hope that helped!!
oh right it was a coin with a glove on it, thanks i've been getting my spoilers from pinterest no wonder there have been many fanart of braun and soleum working on a talk show ╮(￣▽￣)╭
after the tamra train and the doll gets incinerated does braun follow soleum in his host form? no shit braun rly scared the shit outta me there also when soleum gave assistant manager eum haje his third hand as parent plant how does he give the coin if it was inside the rabbit doll i can't remember also i'm lazy