ok

DIdn't you said it was impossible ?
Or did I misunderstood what the morphing is ?

there can be some overlap

Moving an item from Diablo into Hellfire will always recreate the item to the properties it would have had if you had originally acquired it in Hellfire under identical circumstances[1]. Sometimes, the Hellfire rules match the Diablo rules so your recreated item happens to have the same properties it had in Diablo. Other times, it changes in a way you can notice.

For your case of moving an item from SP Diablo to MP Diablo, you have a better chance of the item retaining its statistics, because the item generation rules are much closer between SP/MP versus between Diablo/Hellfire. SP Diablo disallows some items that are only useful in MP, such as scrolls/staves of Resurrect and Heal Other. With no other players in SP, those spells are not useful, so they cannot appear. However, all the standard base items are allowed in both, and almost all magic affixes, so unless the purchased item can have an SP-only affix (such as being a Staff of Resurrect), I expect it would survive the transfer to MP. Bucklers cannot be a Buckler of Resurrect, so the affix list is the same in SP versus MP.

[1]: This includes various things you cannot normally see in game, such as the random number seed, which is effectively impossible to replicate in normal play.

OK thanks you too for explain.