Learn English – Where should the adverb “soon” be positioned

"Let's simply share" and "Let's share simply" have different meanings.

'Let's simply share" has the same meaning as "Let's just share". That is, let's share without any more fuss, or making too much of sharing.

"Let's share simply" has the meaning of sharing in a simple way, that is, to avoid complication which could arise if we were to attempt sharing like "You can have 20% of the cake, and I'll take 35.47%, and the rest will go to Jake." That's bound to bring some sort of trouble.

They have different meanings because the adverb has changed positions. Adverbs can go anywhere. For example:

Simply, let's share
Let's share simply.
Let's simply share.

Each of them means different things, and both of them are grammatically correct.

There are many different kinds of adverbs, and each one has different rules for placement.
This is one reason why knowing that some word "is an adverb" is pretty useless information,
because it doesn't tell you anything about how, when, or why to use it.

Still is a complex temporal quantifier, and refers to temporal continuity from past to present.
Like most quantifiers, it can appear either directly before the constituent it binds (in this case
the constituent some time left), or before any constituent that contains that (in this case the
verb phrase be some time left).

So they're both fine. In this case.
In both speech and writing (anything that works in speech is OK in writing).
Other kinds of adverbs have other rules governing their placement.