The paper is devoted to the information spreading (propagation) on random graphs evolving by a linear preferential attachment (PA) model. The PA is proposed to play a double role, namely, as the evolution model, i.e. the tool to add new edges and nodes to the network and (or) to remove existing nodes and edges, and as the spreading tool. We assume that a single message is to be propagated within a fixed time interval. In practice, a message may become old and not relevant. A node having a message instantaneously passes on information to one of its neighbour nodes which does not have the message yet. This neighbour may be either a node newly appended to the graph or an existing node. By probabilities of $\alpha-$, $\beta-$ and $\gamma-$schemes of the used PA model a new directed edge is drawn between a new node appended to the graph and an existing node or a new edge is drawn between a pair of existing nodes. By convention the propagation is provided if the new node (or one of the existing nodes) without the message has an incoming edge to an existing node having the information. Distributions of the number of nodes that received the message and the total number of nodes as well as the ratio of the latter random numbers in a fixed time interval with regard to parameters of the PA are obtained.