She had her umbrella with her.

Literal

She [topic-は] umbrella [object-を] was-having.

持つ ('to hold, carry, have') in the progressive ~ている form means 'to be in the state of holding/having' — a possession state, not the act of taking up. 傘を持っている ('has an umbrella with her') is the standard way to say someone is currently equipped with one, rather than the abstract 'owns one.' This state-result reading of ~ている is one of the more confusing aspects of the auxiliary for English speakers, who naturally read 'is having' as a progressive action.