Once it is fully charged, the device can be operated on Freneskae to create the Distorted engrammeter during or after Fate of the Gods. After is suggested as you need this version of the Engrammeter for the quest.
After completion of the associated quest, if you have unlocked the entire Hub track, this item can be retrieved from the Quest Item Storage chest at the Quest Point Caravan if lost or destroyed. Otherwise, a new one can be obtained from Kharshai.
Note that creating a Distorted engrammeter completes the "Distorted Div" requirement for the Master Quest Cape and awards you with 25,000 Divination experience. Beyond this, there is no reason to keep this item. As such, it can be destroyed or kept as you desire.