Is the summation correct that the Hereafter should be in the believer's heart, in intention and action, and the world in his hand, in intention and action?

If the Hereafter were in the believer's heart as an intention, and the worldly life in his hand as action, that would be the most correct approach. For intention is an act of the heart, and the worldly life in the hand means that the heart is not attached to it. The best summary for combining the worldly life and the Hereafter is the verse: "But seek, through that which Allah has given you, the home of the Hereafter; and [yet], do not forget your share of the world."