Catalyzes the reversible transfer of the CoA moiety from gamma-butyrobetainyl-CoA to L-carnitine to generate L-carnitinyl-CoA and gamma-butyrobetaine. Is also able to catalyze the reversible transfer of the CoA moiety from gamma-butyrobetainyl-CoA or L-carnitinyl-CoA to crotonobetaine to generate crotonobetainyl-CoA (By similarity). (R)-carnitine + crotonobetainyl-CoA = (R)-carnitinyl-CoA + crotonobetaine (R)-carnitine + gamma-butyrobetainyl-CoA = (R)-carnitinyl-CoA + 4-(trimethylamino)butanoate Amine and polyamine metabolism; carnitine metabolism. Homodimer. Belongs to the CoA-transferase III family. CaiB subfamily.