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Similarly, add a new item to the quest menu, assign it the type OBJECTIVE_KIND_HERO_MUSR_SURVIVE, and specify the script name of the hero as the parameter (Parameters, Add).
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To clarify: Go to MapPropretiesTree, find the string objectives->primary->playerSpecific->0->objectives. There should be one item (0) inside, which corresponds to the quest of capturing a city in 7 days (if you have changed anything there, otherwise it will simply be the "Kill-em all" quest, but that's not the main point). Add a new item there, specifically, right-click on objectives (on this objectives: "objectives->primary->playerSpecific->0->objectives"), and select Add. Then, enter the quest name (Caption), description (Description), type (Kind, I specified which one), and parameter (Parameters, right-click, Add) – the script name of the hero. You can find it by selecting the hero, pressing the spacebar, and going to the Settings tab; it will be written there as "Script name." Good luck!