A Nantucket, Massachusetts judge ordered the three of them to turn the phone over so defense experts could examine it.
Spacey's lawyers claimed in a hearing earlier this month that evidence that could exonerate the 59-year-old actor was deleted from the phone before it was turned over to prosecutors.
"(The accuser) and his family have no memory of seeing the subject phone after December 2017, when that phone was delivered to the Commonwealth," family attorney Mitchell Garabedian wrote in court documents. "(The accuser) and his family have searched all the places where such a phone may have been stored. They have not found the phone."
CNN is not naming Spacey's accuser because he is an alleged sexual assault victim.
Spacey is accused of indecent assault and battery for allegedly groping an 18-year-old busboy in July 2016 at the Club Car bar on the island of Nantucket.
During the alleged assault, the accuser sent text messages on his phone, including a less-than-one-second-long video, to his girlfriend.
Prosecutors told Judge Thomas Barrett last month they obtained a copy of data from the phone, but the device was then returned.
A CD containing the files obtained from the phone was given to defense attorneys, but they say that was not sufficient.
"Access to the underlying databases is necessary to perform a proper analysis, including whether messages may have been deleted or to attempt recovery of deleted data," defense expert Sankara Shanmugam wrote in an affidavit.
Spacey's lawyers argued screen shots and a report by police leave no question evidence was deleted, and they should be allowed to try and recover it.
"He and or his mother deleted the exculpatory texts that were on the phone," defense attorney Alan Jackson said in a hearing this month. "They deleted information that they didn't want the police to have, they deleted information they didn't want us to have."
Garabedian wrote in today's filing that police notes say the phone was returned to the accuser's father, but "he has no memory of receiving his son's phone from the police."
Since the phone cannot be found, Garabedian says they are trying to find backups of what was on it.
"Understanding the significance of this order, (the accuser) and his family are in the process of engaging a digital forensic expert to search for likely backups of (the accuser's) 2015 phone."
In response to Garabedian's filing, Judge Barrett extended the deadline for turning the phone over until July 8.
If the phone is not found by then, the accuser, his mother and attorney must appear in court to testify about its whereabouts.
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