LONDON, Oct 29 (Reuters) - Former British Prime Minister Liz Truss's personal phone was hacked by suspected agents working for Russian President Vladimir Putin when she was foreign minister, the Daily Mail reported on Saturday.Those agents gained access to "top-secret details" of negotiations with international allies in addition to private messages exchanged with Truss's close friend Kwasi Kwarteng, who later became finance minister, the report said.The messages are believed to have included discussions with senior international foreign ministers about the war in Ukraine, including details about arms shipments, it added.The hack was discovered during the Conservative Party leadership campaign that led to Truss becoming prime minister, the Mail reported.The Mail said the messages that fell into foreign hands included criticisms of Johnson made by Truss and Kwarteng, "leading to a potential risk of blackmail"."