The 66-year-old was convicted of nine charges at the Republic of Ireland's non-jury Special Criminal Court in December.
Murphy lives at Ballybinaby, Hackballscross, County Louth, on a farm that straddles the border with Northern Ireland.
He had denied all the charges.
The prosecution was brought after an investigation by the Irish Criminal Assets Bureau (CAB).
Sentencing of the alleged former IRA "chief of staff", Thomas 'Slab' Murphy, has been delayed until 26 February.