<p> We provide estimates of both cross section and rate for the stimulated attachment of a second positron into the (1<i>s</i>² ¹<i>S^e</i>) state of the <i>H&macr; </i>⁺ ion using Ohmura and Ohmura&rsquo;s (1960 Phys. Rev. 118 154) effective range theory, Reiss&rsquo;s strong field approximation (1980 Phys. Rev. A 22, 1786), and the principle of detailed balancing. Our motivation for producing <i>H&macr;</i>⁺ ion include its potential to be used as an intermediate state in bringing antihydrogen to ultra-cold (sub-mK) temperatures required for a variety of studies, which include both spectroscopy and the probing of the gravitational interaction of the anti-atom. We show that both cross section and rate are increased with the use of a resonant laser field.</p><p>