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You have done a fairly good job but it seems wordy. You can concise your write up by eliminating redundant words and elaborate sentences. Pls see the corrections in bold.
I am in the process of applying for my assessment of credentials for which the transcripts are mandatory, (The transcripts are mandatory in my application process and hence I request you to courier them to me as soon as possible to the below mentioned address). So I have to seek your help by immediately couriering the envelope to me at my office address : XYZ, Law Firm, Circle Town, Chennai, India which will enable onward submission of the same within the deadline.
