What's the English equivalent for the Italian slang expression "magna magna"

Quite similar is

have/get one's nose/snout in the trough

British disapproving

to be in or get into a situation in which one is getting or trying to get a lot of money

{Merriam-Webster}

'He's got his nose in the trough' could be applied to any person over-eagerly procuring money, but is almost always used for illegal or at least dodgy practices.

The idiom to feather one's (own) nest fits the bill which means:

(figuratively) to use power and prestige to provide for oneself selfishly. (Said especially of politicians who use their offices to make money for themselves.): 'The mayor seemed to be helping people, but she was really feathering her own nest.' 'The building contractor used a lot of public money to feather his nest."

[McGraw-Hill Dictionary of American Idioms and Phrasal Verbs]

How about "money grab"? As in "That bridge-to-nowhere was a big money grab". It's not exactly the same meaning, but it's close.

In American English, that would probably be "Lining his own pockets" if you mean he's making sure he gets some kind of money at the end. To be more like just stealing from the position, you could say he "has his hand in the till [cash register]".