The phrase "allegedly through" is correct and usable in written English.
It can be used when discussing actions or events that are claimed to have occurred in a certain manner, often implying doubt or uncertainty about the claim.
Example: "The funds were allegedly through a series of complex transactions that raised suspicions."
Alternatives: "reportedly via" or "supposedly through".
He is also alleged to have made millions of dollars from foreign contracts, some of them allegedly through a militia, Kandahar Strike Force, which works for the CIA.
John F Kennedy scraped 112,827 (0.17%) more votes than Nixon nationwide, allegedly through the corrupt intervention of the mayor of Chicago, Richard Daley.
That was when huge traffic jams were created across the highly trafficked George Washington Bridge to and from New York City, allegedly through collusion by certain members of Christie's staff and political appointees.
A relative of Joseph's, Gilbert Chagoury, is probably the most famous figure connected to the village he made hundreds of millions of dollars in Nigeria during the 90s, allegedly through corruption schemes.
The email makes a number of other claims, including that Malcolm Hoenlein, the executive vice chairman of the Conference of Presidents of Major American Jewish Organizations, has been "raising money hand over fist for the Republicans," allegedly through former Virginia Congressman Eric Cantor.
A woman has been charged with two counts of assault and one count of break and enter with intent after allegedly climbing through a Tim Hortons drive through window to beat a pregnant employee.
Georgian police arrested Hayastan Shakarian after she allegedly hacked through a fibre optic cable that runs through Georgia to Armenia, while digging for copper.
The money was allegedly funnelled through a British lawyer, Jeffrey Tesler.
The contract, wildly favorable to B.S.G.R. at the expense of Guinea, was allegedly secured through bribes.
The total amount of government funds allegedly lost through corruption and fraud was estimated to be $100 $250 million.
Shrien, allegedly forced through a window, did not have a scratch on him, and neither did Tongo.
