There is no hope of making sense of this without seeing the context, and even then it is not entirely straightforward. This exact phrase occurs in the last part of The Forsyte Saga by John Galsworthy, which I think must be the source. It refers to the child Jon Forsyte, who is grief-stricken when his beloved nurse, "Da", leaves to get married. Here is the passage:

"'Da', worn out by washing his knees, or moved by that mysterious instinct which forces even nurses to desert their nurslings, left the very day after his birthday in floods of tears 'to be married' — of all things — 'to a man'. Little Jon, from whom it had been kept, was inconsolable for an afternoon. It ought not to have been kept from him! Two large boxes of soldiers and some artillery, together with The Young Buglers, which had been among his birthday presents, cooperated with his grief in a sort of conversion, and instead of seeking adventures in person and risking his own life, he began to play imaginative games, in which he risked the lives of countless tin soldiers, marbles, stones and beans."
http://books.google.es/books?id=eZVuP3gESOgC&pg=PT162&lpg=PT...

The Young Buglers (1880) by G. A. Henty, is a heroic, adventurous account of the Peninsular War seen through the eyes of two orphaned brothers.

So Jon relieves his feelings by carrying out imaginary adventures with the toy soldiers, presumably following the story in the book. The sense of "conversion", which does not seem to have anything to do with a religious conversion here, is presumably related to the part that immediately follows this phrase, about playing imaginary games instead of seeking adventures in person. So I think it must mean that he converts the soldiers into a proxy of himself, a projection of his own person, and plays out adventures with them, imagining he were taking part himself: risking his life to relieve his grief, but safely, through them. So the basic sense would be conversion of the toy soldiers into representations of himself.