Transferring $A_{\mathrm{\infty }}$ (strongly homotopy associative) structures

We give explicit formulas for transfers of $A_{\mathrm{\infty }}$-structures and related maps and homotopies in the most easy situation in which these transfers exist. One half of our formulas was already known to Kontsevich-Soibelman and to Merkulov who derived them, without explicit signs, under slightly stronger assumptions than those made in this note.