To solve this problem, let's break it down step by step, following the given solution closely:

1. Identify the daily greening area during actual work: Let the area greened each day during actual work be $x$ thousand square meters. This is our variable of interest.

2. Calculate the originally planned daily greening area: Since the actual work efficiency each day was 35% higher than originally planned, the originally planned daily greening area would be $\frac{x}{1+35\%}$ thousand square meters. This adjustment accounts for the increased efficiency.

3. Set up the equation based on the task completion time: The task was completed 40 days ahead of schedule due to the increased efficiency. To express this in terms of the greening area, we compare the time it would take to green 800,000 square meters (or 80 thousand square meters, adjusting for the units of $x$) at the planned rate versus the actual rate. This gives us the equation $\frac{80}{\frac{x}{1+35\%}} - \frac{80}{x} = 40$.

4. Simplify the equation: To simplify, we first address the division by a fraction in the first term, which is equivalent to multiplying by its reciprocal. This simplifies the equation to $\frac{80(1+35\%)}{x} - \frac{80}{x} = 40$.

5. Identify the correct equation: Based on the simplification, we see that the equation that matches our derivation is $\frac{80(1+35\%)}{x} - \frac{80}{x} = 40$. This corresponds to option A in the given choices.

Therefore, the correct equation that represents the scenario described in the problem is:

$$\boxed{\text{A: } \frac{80(1+35\%)}{x} - \frac{80}{x} = 40}$$