"He found a way out of his difficulties through the chance (он нашел выход из своих трудностей благодаря случаю) that Sir Charles, who had conceived a friendship for him (когда сэр Чарльз, который испытывал к нему дружеские /чувства/), made him the minister of his charity (сделал его своим поверенным: «исполнителем своей благотворительности») in the case of this unfortunate woman, Mrs. Laura Lyons (в деле этой несчастной женщины, миссис Лоры Лайонс). By representing himself as a single man (представившись холостяком) he acquired complete influence over her (он приобрел полное влияние над ней), and he gave her to understand (и дал ей понять) that in the event of her obtaining a divorce from her husband (что в случае получения ею развода у ее мужа) he would marry her (он на ней женится). His plans were suddenly brought to a head by his knowledge (его планы сразу же окончательно созрели, когда он узнал; to bring to a head — доводить что-либо до конца, заканчивать что-либо) that Sir Charles was about to leave the Hall (что сэр Чарльз собирается покинуть Баскервиль-холл) on the advice of Dr. Mortimer (по совету доктора Мортимера), with whose opinion he himself pretended to coincide (с чьим мнением он сам притворно соглашался; to coincide — совпадать; соглашаться). He must act at once (он должен был действовать немедленно), or his victim might get beyond his power (иначе его жертва могла выйти за пределы его влияния).
friendship ['frendSIp], minister ['mInIst@], charity ['tS&rItI]
"He found a way out of his difficulties through the chance that Sir Charles, who had conceived a friendship for him, made him the minister of his charity in the case of this unfortunate woman, Mrs. Laura Lyons. By representing himself as a single man he acquired complete influence over her, and he gave her to understand that in the event of her obtaining a divorce from her husband he would marry her. His plans were suddenly brought to a head by his knowledge that Sir Charles was about to leave the Hall on the advice of Dr. Mortimer, with whose opinion he himself pretended to coincide. He must act at once, or his victim might get beyond his power.
"He therefore put pressure upon Mrs. Lyons to write this letter (поэтому он заставил миссис Лору Лайонс написать это письмо; to put pressure upon smb. — оказывать нажим/давление на кого-либо), imploring the old man to give her an interview on the evening (умоляя старика встретиться с ней вечером) before his departure for London (перед его отъездом в Лондон). He then, by a specious argument (затем он под благовидным предлогом: «правдоподобным доводом»), prevented her from going (отговорил ее идти; to prevent — предотвращать), and so had the chance for which he had waited (и таким образом получил возможность, которой он дожидался).