'DWTS' Gleb Savchenko Brings Receipts To Child Custody Fight With Ex-Wife

Screenshots or it didn't happen? Gleb Savchenko says he's got 'em ... at least when it comes to his child custody war with his ex-wife.

The "Dancing with the Stars" pro says he has hard proof in his emergency custody battle with Elena Samodanova ... dropping screenshots he says prove she traveled to Moscow with their youngest daughter after keeping the children -- Olivia and Zlata -- in Hong Kong for years.

Gleb filed docs with the alleged proof ... one screenshot appears to show Elena's phone location pinging in Moscow ... while another captures a WhatsApp conversation in which she allegedly says she arrived in Russia for a family funeral. Gleb claims the messages also confirm their youngest was with her.

In his declaration, Gleb says he never consented to the trip -- and didn't even know it was happening. He tells the court he would've objected to Zlata traveling to what he calls a war-torn country ... adding Elena has repeatedly made major decisions involving their daughters without his input.

As TMZ first reported, Gleb is asking a judge for an emergency child custody order, claiming Elena has kept their daughters in Hong Kong since 2023. He also says he's filed a Hague Convention petition -- an international legal request seeking Zlata's return, while he says Elena is arguing Hong Kong has jurisdiction over the custody dispute.

He wants the judge to grant him "temporary sole legal and sole physical custody" of their 15-year-old daughter, Olivia -- with no visitation from Elena -- pending further court involvement after a scheduled hearing.

Meanwhile, Elena tells TMZ Hong Kong is Olivia’s legal home and accuses Gleb of wrongfully keeping her in California by canceling her return flight, saying ... "His emergency filing is a rushed attempt to bypass proper laws. I am asking the court to halt temporary orders and grant a continuance so my counsel can present Olivia’s permanent records through the correct legal channels."