The problem of strategically supported cooperation in 2-person differential games with integral payoffs is considered. Based on initial differential game the new associated differential game (CD-game) is designed. In addition to the initial game it models the players actions connected with transition from the strategic form of the game to cooperative with in advance chosen principle of optimality. The model provides possibility of refusal from cooperation at any time instant t for each player. As cooperative principle of optimality the Shapley value is considered. In the bases of CD-game construction lies the so-called imputation distribution procedure described earlier in (Petrosjan and Zenkevich, 2009). The theorem established by authors says that if at each instant of time along the conditionally optimal (cooperative) trajectory the future payments to each player according to the imputation distribution procedure exceed the maximal guaranteed value which this player can achieve in CD-game, then there exist a Nash equilibrium in the class of recursive strategies first introduced in (Chistyakov, 1981) supporting the cooperative trajectory. In the present paper the results similar to (Chistyakov and Petrosyan, 2011) are obtained without the requirement of independent motions and for the more general type of payoff functions.