Is a company with strong earnings per share always a good investment? 
Why or why not?

No, because earnings can be manipulated via depreciation rates ect

No, because earnings can be manipulated via depreciation rates ect.
The definitive answer can be obtained thru various courses available
from the Association of Certified Fraud Examiners in Austin, TX.

Earnings per share is a commonly known and used value for most stocks.
 Because it's so used, the value of the stock has already taken this
into account.  So if the earnings per share is stronger than it was
before then the price has probably already gone up (and therefore you
can't expect this strength to raise the value even more).
Remember that there are millions of people trying to beat the market
with their brilliant stock picks, so the prices for each stock already
reflect all commonly known knowledge about the company.

An analogy to this question is "Is buying a car with good tires always
a good car buy."  While good tires are important, so is a good engine,
maintenance track history, consumer reports and ratings, reliability,
quality, etc.

EPS is but one of many financial indicators that one should consider
when making investments.  Financial results and condition is an
indication of past performance and a snapshot of one point in time.  A
good past performance is no guarantee of future performance, as many
investment managers will tell you.  It is merely a tool and not a
crystal ball.

Generally speaking, a good EPS is better than a bad one, but is not
the end all, be all. =)

Look at PE (price-to-earnings) ratios to compare different stocks with
differents EPS.

Company A: EPS $0.10, stock price $10. Thus, PE is 100x

Company B: EPS $0.05, stock price $1. Thus, PE is 20x

A lower PE means you're paying less per unit of earnings. In the case
above, Company B is a better investment, even though it has lower EPS.