When the last Swedish possessions in Estonia and Livonia were being threatened by the Russians in 1709-1710 some of the archives were evacuated. One of them was the archive of the Estonian Governor General. It stayed in Sweden for more than a decade. In 1726 or 1727 it came back to Estonia due to the regulations in the Treaty of Nystad. However, some parts were never handed over to the Russians. This means that some incoming letters to Governor General de la Gardie are in Riksarkivet (Livonica II, vol. 270-300) and others in Tartu (as far as the GNW is concerned vol. 1.2.284-291).
When one looks at the individual volumes in Tartu they are quite different. Vol. 284 (first half of 1700) consists of nearly 300 pages, while 291 (1704) is less than 100 pages (all heavily damaged by water). One of the few partly legible items in the latter volume is a letter from Adam Ludvig Lewenhaupt to de la Gardie, dated Mitau 24 September. Lewenhaupt writes of the remarkable successes of the troops under his command and the victory at Jacobstadt. With no more that 3,080 men he had soundly beaten the enemy which lost 5,000 men in dead and wounded (just after the battle Lewenhaupt claimed that 2,000 enemy soldiers had been killed).
In Livonica II there are a few more letters from Lewenhaupt to de la Gardie: 23 May, 6 June, 11 July and 14 September 1703 (all from Mitau). While it's very likely that Lewenhaupt did not write to de la Gardie as often as he did to Frölich in Riga one can safely assume that this means that many letters have been lost.