Moving claim over to at fault party insurance after already sending photos of initial estimate from adjustor

Question,

If I already went through my insurance for not at fault auto claim, sent pictures for photo estimate, and received a estimate offer for repair / total loss from adjustor , is it possible to withdraw the claim (understanding the accident itself will not be withdrawn and will remain on the record), and start the claim process with at fault party instead, effectively canceling out the claim with my insurance ?