a currency depreciation at full capacity does result in a decline in the value of domestic assets. this decline in savers’ real wealth will induce an increase in saving to rebuild wealth, initially improving the balance of trade from the currency depreciation. As the real wealth of savers increases, however, the positive impact on saving will decrease, eventually returning the economy to its previous state and balance of trade.
In the absorption approach, think about excess capacity. Basically to reduce your trade balance deficit you will need your income to grow relatively more than your expenditures. If the economy is below full employment (ie there is excess capacity), domestic consumption will increase, and domestic production as well (to match foreign and domestic absorptions). Since Marginal Propensity to Save is not 0, Y will grow relatively more than E, hence the trade deficit reduces. If, however, we are operating at a level above full employment, the price level will increase because of the domestic and foreign demands have increased. An increase in the domestic price level will bring back the real exchange rate back to the initial level, and the trade deficit will not improve.
The extract you used basically tells you that as depreciation occurs, net wealth falls and induces people to save more (private savings increase and trade deficit reduces). But as soon as their net wealth is back to its original level, they will start spending again, and price levels will increase (we are not in excess capacity here), and eventually they will go back to import as much as they did before, and the trade balance goes back to its initial level.