Should the worshiper immediately complete his prayer upon the call for the funeral prayer while he is making up for a missed Dhuhr prayer?

After the Imam says the salām, complete the parts of the prayer you missed. Do not interrupt the obligatory prayer for the funeral prayer (which is a communal obligation - fard kifāyah). After you finish the Dhuhr prayer, join the congregants praying over the deceased to earn the reward.