The high-temperature crystallizing phases of fluxes (molten solutions) based on Bi2O3:MoO3 = 1:3 and diluted by Na2CO3 and B2O3 (under varying of Na2CO3:B2O3), and by CuO and Mn2O3 (0 <= Mn2O3:CuO <= 5) are studied. The conditions of the stable crystallization of Mn1-x2+CuxMoO4, Mn23+O3, Mn2+Mn23+O4, Mn1-x2+CuxMn3+BO4 and Mn2-x2+CuxMn3+BO5 have been found. The influence of MoO3 and Na2CO3 to the crystallization processes of Mn2+ - and Mn3+ -containing Mn1-x2+CuxMoO4 and Mn2+Mn23+O4 and Mn23+O3 are clarified. The occurrence of the chemical bonds of these types at the crystallization of Mn-heterovalent Mn1-x2+CuxMn3+BO4 and Mn2-x2+CuxMn3+BO5 oxyborates is studied. Single crystal growth techniques of these oxyborates are suggested. The results of the structural and magnetic characterization of some discussed compounds are presented.