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Every [anonymous] question asked in the responsum Torah Lishmah ends with an address to the answerer and the abbreviation ושכמ"ה (e.g.). The Otzar Rashei Teivos had only one entry for this abbreviation (without the initial conjunction), which was "שכרו כפול מן השמים" - "his reward is multiplied from heaven".
Torah Lishmah is an interesting and atypical sefer to begin with. It was written by the Ben Ish Chai under the pseudonym Yechezkel Kachali (note that the gematria of Yechezkel = Yosef and the gematria of Kachali = Chaim, which is the Ben Ish Chai's name). For all we know, these questions were all made up by the author himself (Terumas HaDeshen style) just for the purpose of demonstrating the answer. In that case the common language would obviously be more than just "editorial uniformizing."
As for the expression itself, I had assumed it went hand in hand with the words that typically precede it, יורנו המורה לצדקה. It could be a way of saying: Even though we are not compensating you for your time, please answer our query as tzedakah, and Hashem should repay your efforts doubly. Of course, knowing the Ben Ish Chai, there are probably kabbalistic layers of meaning to these phrases, but I think my theory is close to the "pshat."
