Based upon what you have written (including comments)
You are a visa national from Nigeria who applied for entry clearance
as a visitor
You did not include supporting documents to show your financial
You did not explain why you previously stayed in the UK significantly
beyond the intention you stated in a previous application
You used an alias whilst previously in the UK and provided no
You did not disclose a criminal history
And two weeks after this refusal you want to make a fresh application that includes an invitation and a letter of explanation that you have prepared. And your question is if you are likely to be successful.
No. Decidedly not. You won't be back for quite some time. If ever...
The last two items in my list indicate that your next application may attract a ban under Paragraph 320 of the rules, which says in part...
(iv) using deception in an application for entry clearance, leave to
enter or remain or in order to obtain documents from the Secretary of
State or a third party required in support of the application (whether
successful or not); and
there are other aggravating circumstances, such as absconding, not
meeting temporary admission/reporting restrictions or bail conditions,
using an assumed identity or multiple identities, switching
nationality, making frivolous applications or not complying with the
(bold face mine)
There is no discretion where Paragraph 320 is concerned. It is a mandatory ground for refusal.
Finally, you're wasting time trying to use the internet to resolve a stream of judgement failures that have brought unimaginable complexity to your case. There's only about a dozen solicitors in the UK who can successfully navigate Paragraph 320, and none of them appear as random people on the net. Use the Law Society to instruct a qualified solicitor to help you... http://solicitors.lawsociety.org.uk/