LONDON, June 12 (Reuters) - Mexican magnate Carlos Slim

has taken a 3.16% stake in BT, Britain's biggest

broadband and mobile operator, according to a stock market

filing on Wednesday, in a boost to the company's new chief

executive Allison Kirkby.

The stake bought by Slim, whose family controls

telecommunications giant America Movil, has a market

value of about 408 million pounds ($522 million), based on BT's

closing share price on Wednesday.

Slim acquired the holding through his Inbursa financial

company and two other group companies.

Shares in BT rose by more than 10% last month after Kirkby

set out her ambition to more than double free cash flow over the

next five years, cut more costs and potentially dispose of its

global enterprise business.

A BT Group spokesperson said the company welcomed any

investor who recognized the long-term value of its business.

"We have frequent communication with all of our shareholders

and meet with major investors on a regular basis," the

spokesperson said. "We look forward to engaging with Inbursa,

just as we do with all investors."

($1 = 0.7816 pounds)