What is the best way to move large amounts of fully declared (“white”) money between countries without being taxed twice?

Legally if both countries slap a tax, then it becomes very hard to do so. You would have to go out of your way to find some type of a scheme in the beneficiary country where the funds will be parked.

You would seek out if the Government offers any exemption to the taxes for purposes of say FDI, Inward Remittance or surrendering the Foreign Exchange and opting for the local currency.