In narrations we read prayers without paying alms are not accepted. Like a locomotive on track that only has a single rail, it cannot move.
So yes, connecting with Allah SWT (through prayer) and with creation (through paying alms) are like a pair of wings to fly with spiritually. Flying with one wing just won’t work.
The Prophet SAWA would eject those who come to the mosque to pray but do not pay their alms.
So even if it’s just one minute before nightfall, there is no right to break the fast. Likewise, prayers cannot be shortened (except in certain circumstances).