Police Scotland has submitted a report to prosecutors following the arrest of Peter Murrell, the former SNP Chief Executive.
In a statement on Thursday afternoon, the Crown Office and Procurator Fiscal Service also confirmed that investigations involving Nicola Sturgeon and MSP and ex-SNP treasurer Colin Beattie were still ongoing.
Mr Murrell - the husband of Ms Sturgeon - was initially arrested on 5 April 2023 before being released without charge, pending further inquiries were carried out.
Last month he was rearrested and charged in connection with embezzlement of party funds.
Police Scotland said they had "submitted a standard prosecution report to the Crown Office and Procurator Fiscal Service in relation to a 59-year-old man who was charged on 18 April, 2024, in connection with the embezzlement of funds from the Scottish National Party."
“Investigations continue and we are unable to comment further," the force added.
Mr Beattie was also arrested in April last year, while Ms Sturgeon was arrested on 11 June 2023. Both were subsequently released.
The Crown Office will now study the police report and decide if there is enough evidence to prosecute Mr Murrell and if such a prosecution is in the public interest.
A spokesperson for the COPFS said: "A standard prosecution report has been received by the Crown Office and Procurator Fiscal Service from Police Scotland in relation to a 59-year-old man and incidents said to have occurred between 2016 and 2023.
"Connected investigations of two other individuals, a man aged 72 and a 53-year-old woman, remain ongoing.
"Professional prosecutors from COPFS and independent counsel will review this report.
"They will make decisions on the next steps without involving the Lord Advocate or Solicitor General.
"All Scotland's prosecutors operate independently of political influence.
"Before deciding what action to take, if any, in the public interest, prosecutors will consider if there is enough evidence.
"There must be evidence from at least two separate sources to establish that a crime was committed and that the person under investigation was the perpetrator.
"This evaluation will involve a thorough examination of the numerous witness statements and extensive evidence collected by police.
"Prosecutors may instruct the police to conduct further investigations before taking a decision.
"Decisions on how to proceed are taken by prosecutors acting independently and are based upon available evidence, legal principles, and the merits of each case.
"They are not influenced by political events."
Operation Branchform was triggered after complaints over how £660,000 of donations given to the SNP to fight an independence referendum were used.
When Mr Murrell was first arrestted officers searched the home he shares with Ms Sturgeon in Glasgow, and the SNP's HQ in Edinburgh.
A £110,000 luxury motorhome was also seized by police from outside the home of Mr Murrell's mother in Dunfermline.
A spokesperson for the SNP said: “It would be inappropriate to comment while a police investigation continues.”
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