In this paper, we consider the message forwarding problem that consists in managing the network resources that are used to forward messages. Previous works on this problem provide solutions that either use a significant number of buffers (that is n buffers per process, where n is the number of processes in the network) making the solution not scalable or, they reserve all the buffers from the sender to the receiver to forward only one message. The only solution that uses a constant number of buffers per link was introduced in [CDLPV10]. However the solution works only on a chain networks. In this paper, we propose a snap-stabilizing algorithm for the message forwarding problem that uses a constant number of buffers per link as in [CDLPV10], but works on tree topologies.